ISWS/Rl-91/79
REPORT OF INVESTIGATION 91
STATE OF ILLINOIS
ILLINOIS INSTITUTE OF NATURAL RESOURCES
Hydraulics of Flow
in the Kaskaskia River, Illinoisby NANI G. BHOWMIK
ILLINOIS STATE WATER SURVEY
URBANA
1979
REPORT OF INVESTIGATION 91
Hydraulics of Flow
in the Kaskaskia River, Illinoisby NANI G. BHOWMIK
Title: Hydraulics of Flow in the Kaskaskia River, Illinois
Abstract: The hydraulics of flow was investigated at two reaches in the Kaskaskia River. The dis-charge varied from 58 to 4000 cfs and the flow frequency varied from 5 to 88 percent. The headloss varied from 0.96 ft/ mile for high flows to 1.98 ft/mile for low flows. The vertical velocity dis-tribution was found to follow a logarithmic distribution. A theoretical distribution predicted thelateral velocity distribution in the bends reasonably well. In all, 79 isovels were developed for allflow conditions. The average value of the energy coefficient was 1.45 for straight reaches and 1.43for bends. Similarly, the average value of the momentum coefficient was 1.22 for straight reachesand 1.18 for bends. Manning’s roughness coefficient varied from 0.039 to 0.053. During low flows.the river flows through a series of pools and riffles. The median diameter of bed materials variedfrom 40 mm in the riffle to 0.04 mm in the pool, whereas the Froude number changed from 0.7 to0.01. During high flows, the effect of the pool and riffle on the flow condition is minimal or non-existent.
Reference: Bhowmik, Nani G. Hydraulics of Flow in the Kaskaskia River, Illinois. Illinois StateWater Survey, Urbana, Report of Investigation 91, 1979.
Indexing Terms: Bed materials, circulation, hydraulic properties, hydraulics, head loss, Illinois,Kaskaskia River, low flow, open channel flow, pools, riffles, river flow, roughness (hydraulic).
STATE OF ILLINOISHON. JAMES R. THOMPSON, Governor
INSTITUTE OF NATURAL RESOURCESFRANK H. BEAL, M.U.P., Director
BOARD OF NATURAL RESOURCES AND CONSERVATION
Frank H. Beal, M.U.P., Chairman
Thomas Park, Ph.D., Biology
H. S. Gutowsky, Ph.D., Chemistry
Stanley K. Shapiro, Ph.D., Forestry
Laurence L. Sloss, Ph.D., Geology
John C. Guyon, Ph.D.,Southern Illinois University
William L. Everitt, E.E., Ph.D.,University of Illinois
STATE WATER SURVEY DIVISIONWILLIAM C. ACKERMANN, D.Sc., Chief
URBANA1979
(11-79-1000)lM—12-7—46490
Printed by authority of the State of Illinois
CONTENTSPAGE
Abstract........................................................................................................................................................... 1Introduction..................................................................................................................................................... 1
Plan of the report........................................................................................................................................ 2Acknowledgments...................................................................................................................................... 2
Background analyses ....................................................................................................................................... 2Flow in straight reaches.............................................................................................................................. 3
Velocity structure ................................................................................................................................. 3Resistance to flow ................................................................................................................................ 4Head loss ............................................................................................................................................. 6Hydraulic geometry of alluvial channels................................................................................................ 7
Flow around bends ..................................................................................................................................... 8Superelevation...................................................................................................................................... 8Velocity structure ................................................................................................................................. 9Secondary circulation. .......................................................................................................................... 10Energy dissipation. ............................................................................................................................... 11Bed topography .................................................................................................................................... 11
Pools and riffles ......................................................................................................................................... 11Data collection................................................................................................................................................. 12
Hydraulic geometry of the reaches .............................................................................................................. 12Velocity distribution and water surface profiles. .......................................................................................... 15Bed and bank material samples................................................................................................................... 17
Analysis and results ......................................................................................................................................... 20Geomorphology ......................................................................................................................................... 20Bed material sizes ...................................................................................................................................... 22Hydraulic and geometric characteristics of the reaches ................................................................................ 23Flow frequencies........................................................................................................................................ 29Water surface profiles................................................................................................................................. 30Velocity distribution................................................................................................................................... 30
Vertical velocity distribution................................................................................................................. 30Average velocity in the individual verticals ........................................................................................... 32Average velocity and bottom velocity.................................................................................................... 34Velocity structure, isovels..................................................................................................................... 35
Reach1 ........................................................................................................................................... 35Reach2 ........................................................................................................................................... 53
Flow around bends ..................................................................................................................................... 68Superelevations .................................................................................................................................... 69Secondary circulation ........................................................................................................................... 72
Energy and momentum coefficients ............................................................................................................ 74Roughness coefficient, head loss, and energy dissipation ............................................................................. 75Distribution of unit discharges .................................................................................................................... 80Turbulence in an open channel.................................................................................................................... 82Low flow characteristics: Pools and riffles .................................................................................................. 83
Summary and conclusions................................................................................................................................ 91References....................................................................................................................................................... 92Notations......................................................................................................................................................... 94Appendices...................................................................................................................................................... 96
The average value of the energy coefficient was 1.45 for straight reaches and 1.43 for bends.Similarly, the average value of momentum coefficients was 1.22 for straight reaches and 1.18 forbends. Average Manning’s roughness coefficients varied from a minimum of 0.039 to a maximum of0.053. Roughness coefficients showed a decrease in value with an increase in discharge. Analysesshowed that unit discharges across the width of the river for various flow conditions are proportionalto the respective water depths in the section.
During low flows, the Kaskaskia flows through a series of pools and riffles with larger diameterbed materials in the riffle and fine materials in the pool. The median diameter varied from 40 mmin the riffle to 0.04 mm in the pool. The Froude number varied from 0.7 in the riffle to 0.01 in thepool. Head loss was about 2.48 ft/mile in one pool-riffle sequence and about 4.44 ft/mile in another.During high flows, the pools and riffles are all submerged and their effects on the overall flow con-dition are minimal or nonexistent.
The hydraulics of flow was investigated at two reaches in the Kaskaskia River. Hydraulic data werecollected for 58, 1040, 1420, and 4000 cfs from Reach 1 below Lake Shelbyville and for 290, 2160,and 3700 cfs from Reach 2 below Carlyle Lake. The flow frequencies varied from 5 to 88 percent.In all, 79 bed and bank material samples were collected and analyzed to determine the particle sizedistribution. In all cases, the flow can be approximated by uniform flow equations. Head loss variedfrom 0.96 ft/mile for high flows to 1.98 ft/mile for low flows. The vertical velocity distribution wasfound to follow a logarithmic distribution. The average velocity at 0.5 foot above the bed was ap-proximately 95 percent of the average velocity in the cross section. Altogether 79 isovels, or lines ofequal velocity, in the cross sections were developed on the basis of the hydraulic data collected in thefield.
The ratio of the maximum velocity to the average velocity remained almost unchanged for low,medium, and high flows. The maximum average velocity was about 145 percent more than the averagevelocity. In a few cross sections, a considerable amount of bed scour took place during high flows.
A theoretical distribution was found to predict the lateral velocity distribution in the bends satis-factorily. The magnitude of the superelevation in the bends was small. At least 3 theoretical equationspredicted the superelevation within the same percent of accuracy. Direction, pattern, and the numberof secondary circulation cells in the bends and in the straight reaches can be sketched from the isovelsdeveloped.
INTRODUCTION
The hydraulics of flow in a natural channel is a functionof numerous variables. Some of these variables can beidentified and accounted for easily; however, some of themare not yet fully understood. In a laboratory experiment,many of the variables can be controlled and adjusted tostay within some prescribed limits. However, in nature, it isan exception rather than a rule to have a controlled flowcondition where the numerical values of different flowvariables remain constant. Flow in a river or stream is neversteady nor uniform, and rarely will one find a straightprismatic channel in which to conduct experiments.
An understanding of the hydraulics of flow must havebeen known to mankind for a long time. Ancient irrigationsystems that are now abandoned in various parts of theworld are a testimony to this fact. Men learned either fromexperimentation or from trial and error how to divert water
from natural streams to irrigate their land. Basic theories ofhydraulics of flow must have started with these initial ex-periments or observations.
Most of the hydraulic data that have been collected fromthe field by various researchers are basically for one set ofconditions and for a single discharge. Rarely has any inves-tigator collected field data from the same stream or riverand from the same location for various flow conditions.The hydraulics of flow in natural stream-segments undervarying degrees of flow conditions has not been studied inany detail. The mechanics of flow in the stream may ormay not show any significant variation as the dischargechanges with changing stages. Thus it is believed that aninvestigation of the flow hydraulics in a natural river forvarious discharges will be of great importance to explain,to verify, or to understand the hydraulics of flow in such
1
Hydraulics of Flowin the Kaskaskia River, Illinois
by Nani G. Bhowmik
ABSTRACT
a stream. On the basis of this premise, two segments of the Stall both before and after his retirement. He also reviewedKaskaskia River in Illinois were selected, monumented, and this report and made many valuable suggestions for its im-surveyed. In all, seven sets of hydraulic data were collected provement.and analyzed, and the results are presented in this report. The project was completed under the supervision of
The segments of the river selected contained both Richard J. Schicht, present Head of the Hydrology Section.straight reaches and bends. The river flows through an Mr. Schicht also reviewed the report and has made a num-erodible channel, typical of many streams in Illinois. ber of suggestions for its improvement. Misganaw DeMissie,Greater understanding of the mechanics of flow in natural graduate assistant, made several field trips and helped inrivers will enable engineers and planners to better manage the collection and analysis of the data, and in the prepara-
the waterways and maintain them against excessive erosion tion of this report. John Lardner, James Harry, and William
or bank caving. Bogner of the Water Survey helped in the field data col-The work described here required planning and execu- lection program.
tion over a considerable period of time. The results should Partial support for the project was provided by the Divi-have valuable applications in the field and should be of sion of Water Resources, Illinois Department of Transporta-value to design engineers and planners alike. tion.
Dodson-Van Wie Engineering and Surveying, Mattoon,Illinois, installed the monuments and surveyed the reach of
Plan of Report the river downstream of Lake Shelbyville. The same firm
This report is divided into four main sections. The first also helped in the data collection at that reach. Givenrod-
section discusses the background analyses needed for the in- Lipe, Inc., Benton, Illinois, installed the monuments and
vestigation. The second section describes the procedures surveyed the reach downstream of Carlyle Lake, and helped
followed in the collection of field data. The analyses in the data collection program at this location. The U.S.
of the data are presented in the third section and the fourth Army Corps of Engineers was very cooperative in maintain-
section summarizes the results of the investigation. Also ing more or less a steady release from both Shelbyville and
provided are listings of the references cited and the nota- Carlyle Lakes during the data collection program. The
tions for symbols used throughout the report. The basic reservoir manager at Carlyle Lake was always helpful in
hydraulic data collected and analyzed for the report are lending boats or other equipment whenever they were
presented in the Appendix. needed. The District and Subdistrict offices of the U.S.Geological Survey at Champaign and Mt. Vernon, respec-tively, loaned a complete set of stream gaging equipmentand provided one of their field personnel, Bill Nyberg,
Acknowledgments for all the field trips.This work was completed as a part of the regular work M a n y p a r t - t i m e s t u d e n t s f r o m t h e U n i v e r s i t y o f
of the Illinois State Water Survey and under the administra- Illinois helped in the field data collection and analysis oftive guidance of Dr. William C. Ackermann, Chief. The in- the data. Students who assisted are: Chong Mook Park,vestigation was initiated a few years ago under the guidance Jeffrey C. Elledge, Kenneth S. Brask, Victor S. Francis,of John B. Stall, Engineer Emeritus and previous Head of and Uday S. Vora. Illustrations were prepared by John W.the Hydrology Section. Most of the initial planning, basic Brother, Jr., William Motherway, Jr., V. Patil, and K. Bajor.data, and analyses were completed before Mr. Stall retired. Ginny Noel and Pam Lovett typed the rough draft ofThe author had many valuable discussions, exchanges of the repor t . J . Loreena Ivens edi ted the repor t , andideas, suggestions, inspiration, and encouragement from Mr. Marilyn J. Innes prepared the camera copy.
BACKGROUND ANALYSES
The flow of water in sand bed alluvial channels has beenstudied by a number of researchers for a long time. Most ofthe major rivers of the world flow through alluvial materialsconsisting mostly of sand and silt. The mechanics of flow ina deformable channel is different from that in a fixedboundary channel. In a sand bed channel, the flow velocity,the turbulence associated with the flow velocity, and the
patterns of the secondary circulation all have the capabilityand the opportunity to mold the shape of the channel. Theshapes of the natural channels are never geometricallyregular. The flow in a natural channel is obviously affectedby so many variables that a clear, straightforward analysisis not possible unless one resorts to some acceptable sim-plification and assumptions. Researchers have been trying
2
to express the characteristics of flow in an alluvial channelwith some theoretical relationships based on the laws ofnature. In many instances the attempts were successful,whereas others met with failure.
The end product of all the constraints in an alluvialchannel is the development of a velocity distribution inboth the lateral and the vertical directions. These velocitydistributions vary in time and space. The longitudinal watersurface slope, or the hydraulic gradient, also constantlyadjusts to reflect the constraints of the channel geometryon the flow in a natural channel. The variability of thewater surface profile is more pronounced for flow around abend than it is for a straight reach of the river.
The theoretical treatment of flow in an alluvial channelcan be divided into two broad divisions, namely, flow instraight reaches and flow around bends. Some of the im-portant contributions related to flow in alluvial channelsare described in the following subsections.
Flow in Straight Reaches
Velocity Structure
Figure 1 depicts the flow in an open prismatic channel.
The prismatic channel is defined as a channel with constantbed slope and unvarying cross-sectional shape. The theoret-ical relationships for open channel flow that have been de-veloped by various investigators are normally applicable forprismatic channels. The velocity distribution equation atany vertical in a prismatic channel can be developed starting
with the Navier-Stokes equation (Lamb, 1945).With Reynolds method of averaging, the Navier-Stokes
equation for turbulent flow of an incompressible fluidbecomes
(1)
wheredensity of the fluid
mean velocity in the i th, jth directionst i m edistance in the ith, j th directionsbody force in the ith directionpressure forcedynamic viscosity of waterReynolds stress
The continuity equation is:
(2)
Equation 1 can be integrated for steady, uniform two-di-
mensional open channel flow with constant fluid properties.The x-component of equation 1 (x-axis parallel to the in-vert slope and positive in the downstream direction, figure
1) is given by the following equation.
(3)
Here ø is the inclination of bed slope, γ is the unit weightof water, µ is the dynamic viscosity of water, and du/dy isthe rate of change of u with y. If we substitute sin ø a sequal to the bed slope So, and assume that laminar frictionis negligible compared with Reynolds stress, i.e., µ (du/dy)
and that this assumption is valid except for veryclose to the boundary, equation 3 becomes
(4)
If we use Prandtl’s mixing length theory with a constantvalue for von Karman’s universal constant k, equation 4can be further integrated and simplified. With this simplifi-cation, equation 4 becomes
(5)Here v is the point velocity at a depth y from the bottom,ks is the equivalent roughness length, V * is the shearvelocity, and A1 and B 1 are constants to be evaluated fromfield and experimental data.
Many researchers have proposed different numericalvalues for the coefficients A1 and B 1 . Most of the originalwork was done for rigid boundary channels. In open chan-nel flow, it is much easier to determine the average velocity
, the average depth , or hydraulic radius R in a cross sec-tion than the values of point velocity v and the point depthy. Here hydraulic radius R is defined as the ratio of thecross-sectional area to the wetted perimeter.
Keulegan (1938) , us ing the exper imenta l da ta of
Nikuradse, has proposed the following equation intendedto be valid for practical open channel flow problems.
(6)
In this analysis von Karman’s universal constant k was as-sumed to be 0.4 and ks was taken to be the average rough-ness height of a bed composed of uniformly compactedsand. Burkham and Dawdy (1976) have indicated thatequation 6 should be valid for turbulent flow in alluvialchannels.
In order to estimate a numerical value of k s for variousflow conditions in an open channel, researchers have
turned their attention to the size distribution of the bedmaterials. Leopold et al. (1964) have proposed use of thed 84 size as the value of k s for flow in channels with beds ofcoarse grained materials and have obtained the followingequation.
(7)
Here d 84 is the size of the bed materials where 84 percentof the bed materials are finer than this size. Richardson(1965) used the d 85 size of the bed materials as the equiva-lent roughness height and replaced ks by d 85 in an equationsimilar to equation 5. He found that the relationships re-
3
Figure 1. Flow characteristics in a prismatic open channel
mained valid for plane bed, ripples, and dune bed channelswith and without appreciable sediment load. Bhowmik(1968) has shown that the d 85 size can replace ks in equa-tion 5 for alluvial channels stabilized with riprap particles.For a set of data from an irrigation canal, equation 8 pre-
dicted the velocity distribution in any vertical quite well(Bhowmik, 1968).
v/V * = 6.96 + 5.11 log(y/d8 5 ) (8)
Sentürk (1978) proposed an equation similar to equation6 where d 35 and d50 sizes of the bed materials were used asthe equivalent roughness length. The equation proposed bySentürk (1978) was postulated to be valid for lower flowregimes (Simons and Richardson, 1961) in alluvial channels.Burkham and Dawdy (1976) have concluded that an equa-tion similar to equation 6 with the d95 size as the equivalent
4
roughness height replacing ks should be a better estimator
of the resistance to turbulent flow in an open channel.
Resistance to Flow
Equations 6 through 8, or any other equation similar tothem, are also designated as the resistance to flow equationin an open channel. Flow resistance in an alluvial channel isa function of many variables (Simons and Richardson, 1971).Some of the important ones are: velocity V, depth D, slopeof the energy grade line Se, density of the water-sedimentm i x t u r e f , dynamic viscosity of the water-sedimentmixture µ, gravitational constant g, fall diameter of the bedmaterial d f , standard deviation σ , shape factor of the par-ticles Sp , shape factor of the reach of the river SR , shapefactor of the cross section of the river S c, and seepage forceon the bed of the river fss.
These variables in turn will determine the bed form in analluvial channel flowing on a sand bed. There are abouteight different types of bed forms that may be present inan alluvial river. These bed forms are shown in figure 2(Simons and Richardson, 1971) for bed materials havinga median diameter d
50less than 0.6 mm. Whenever the
median diameter is more than 0.6 mm, dunes will formrather than ripples after the bed materials begin to move.
The first three bed forms shown on the left side of figure2 are called “lower flow regime.” The last bed form on theleft side is called washed-out dunes or the transition zone,and the four bed forms on the right side are called “upperflow regime.”
In the lower flow regime, the resistance to flow is largeand sediment transport is small. For most of the stablechannels formed in alluvial materials, the dominant featureof the bed form is “dunes with ripples superimposed.”Total resistance to flow is a function of the bed rough-ness. On the other hand, in the upper flow regime, theresistance to flow is small but the sediment transportis large and the Froude number F, is usually greater than 1.The Froude number expresses the ratio between the inertiaforce and the gravitational force and is given by equation 9shown below.
F = V/(gD) 1/2 (9)The flow passes through a critical stage whenever the nu-merical value of F is 1.
In a sand bed channel the bed forms that can develop forany flow condition may or may not remain the same acrossthe whole width of the channel. In some instances, the bedform can be a combination of ripples, dunes, or plane anddunes as one passes from one side of the river to the other(Simons and Richardson, 1971). This was observed in alarge river during low flow stages. The median diameter d 5 0
of the bed material was 0.17 mm.Turbulent flow in a rigid boundary open channel is
independent of the viscous drag, i.e., the viscosity of thewater has minimum effect on the flow resistance in thechannel. However, this is not really true in the case of flowin alluvial streams with sediment movement. Here theviscosity of the fluid may change because of the change inwater temperature or the change in the concentration offluid-sediment mixture. This change in viscosity maychange the bed form, which in turn will change the re-sistance to flow. Thus, a sand bed channel which has adune bed during summer or fall may change to a plane bedduring the late fall as the temperature decreases. This wasfound to be true for the Missouri River between Sioux City,Iowa, and Omaha, Nebraska (U.S. Corps of Engineers,1968) where the average depth decreased by about 1 footfor the same discharge when the temperature dropped byabout 31 degrees Fahrenheit in a period of 1 month. Thebed form was found to have changed from dune bed to
plane bed indicating a decrease in the magnitude of the re-sistance to the flow.
This short analysis indicates that the determination ofthe resistance to flow in an alluvial sand channel is a verycomplex subject. The true effects of the various variablesare not yet fully understood. Attempts have been made
by a number of investigators to estimate a resistancecoefficient for flow in an open channel. One of the simplestequations is the Darcy-Weisbach (Chow, 1959) formula,This formula was developed for flow in pipes. The Darcy-Weisback friction factor f is given by equation 10.
(10)
Equation 10 can be also be written as(11)
where V* is the shear velocity and is equal to (gRS e)1 / 2 By
manipulating equation 11 one can obtain
(12)
Thus, the right hand side of equations 6 or 7 can be takento be equal to (8/f) 1 / 2 . This indicates a direct relationshipbetween the vertical velocity distribution in the stream andthe friction factor f.
Simons and Richardson (1971) have indicated that thevariables Se, D, df
ω , g, and f will determine not only themagnitude of f but also the bed configuration in an alluvialsand bed channel. Here ω is the fall velocity of the bedmaterial and the other variables are as defined previously.
Two of the most widely used equations in open channelflow are Chezy’s and Manning’s equations. These equationsare called uniform-flow formulas and are used to computethe average velocity in a stream when hydraulic and geo-metric characteristics are either estimated or measured inthe field. Chezy’s formula is given by equation 13.
(13)
where C is a factor indicating the resistance to flow and is
also called Chezy’s C. Equation 13 can be modified asfollows.
Therefore,and from equation 12 we obtain
(14)
Equation 14 indicates that Chezy’s C, Darcy-Weisbach fric-tion factor f, and the ratio of the mean velocity to the shearvelocity are all interrelated.
Manning’s equation given by equation 15 below is one ofthe most widely used equations in river hydraulics aroundthe world.
(15)
where n is the coefficient of roughness and is also calledManning’s n. Comparison of equations 13 and 15 indicates
5
Figure 2. Typical bed forms in an alluvial sand bed channel
that Chezy’s C is related to Manning’s n by equation 16.
(16)
Therefore
(17)
It must now be clear that all the resistance-to-flow equa-tions described so far are related to one another in someway.
Over the last 50 to 70 years researchers have worked todetermine the numerical values of n for anticipated flowconditions in open channels. Chow (1959) has summarized
most of the research work that was done up through themid-1950s. He has shown a number of photographs of flowin open channels with corresponding n values. Barnes (1967)also has compiled a list of n values for flow conditions inchannels of varied characteristics which are shown by colorphotos of the flowing stream.
Head Loss
The head loss between two cross sections in an openchannel is normally computed by determining the totalenergies between the respective sections (figure 1). Accord-
6
ing to Bernoulli’s principle, the total energy at section 1(figure 1) should be equal to the total energy at section 2plus any head loss that may have occurred between thesetwo sections.
The term V² /2g in equation 18 is called velocity head.Lateral velocity distribution in an open channel is neveruniform and the velocity head computed by V² /2g is usual-ly smaller than the actual velocity head in the cross section.It is usual practice to compute the velocity head by the re-lationship α V² /2g, where α is known as the energy coef-
ficient or Coriolis coefficient. The value of α was shownto vary from 1.03 to 1.36 by Chow (1959) and from 1.03to 4.70 by Hulsing et al. (1966). The technique for comput-ing the value of α based on field data is given by Chow
(1959).The nonuniformity of velocity distribution across a cross
section also affects the determination of the momentumflux in an open channel. The momentum M of the fluidpassing a cross section per unit time is given by equation 19.
(19)
w h e r e β i s k n o w n a s t h e m o m e n t u m c o e f f i c i e n t o rBoussinesq coefficient, γ is the unit weight of water, Q isthe discharge, is the mean velocity, and g is the gravita-tional constant. Chow (1959) has indicated that for a fairlyuniform straight prismatic channel the value of β varies ap-proximately from 1.01 to 1.12.
Bernoulli’s energy equation is used to obtain equation18 for determining the head loss between sections 1 and 2in figure 1.
(18)
It is assumed that the bed slope is very small and as suchthe depth of water in a direction normal to the bed is ap-proximately the same as the depth of water in the vertical
direction. In case of uniform flow‚ Se = S w = So . However‚in natural channels‚ flow is never uniform and graduallyvaried flow equations must be used to describe the flowvariability.
Hydraulic Geometry of Alluvial ChannelsThe average velocity ‚ the average depth ‚ width W,
and hydraulic gradient Se are some of the parameters term-ed the hydraulic geometry parameters at a cross section inan alluvial channel. There are three different methods thatcan be used to determine the hydraulic geometry parametersin streams and rivers. These are:
1) Tractive force method2) Permissible velocity method3) Regime concept method
In the tractive force method, the allowable shear forceexerted by the flowing water on the bed and bank of thestream is estimated. With known values of tractive force,
measured bed and bank slopes, and measured bed and bankmaterial sizes, the stability of the bed and the bank is testedand a stable geometry of the stream is determined. One ofthe foremost methods for de termining the hydraul icgeometry of open channels based on tractive force is givenby Lane (1955). Lane’s method is valid for streams andrivers flowing through coarse or fine alluvial materials.
In the permissible velocity method, an allowable or per-missible velocity is estimated on the basis of the size distri-bution of the bed and bank materials. The relationships be-tween the permissible velocity and the bed and bank mate-rial sizes are given by Lane (1955), Chow (1959) andothers. If the existing average velocity in the stream crosssection is larger than the estimated permissible velocity,then it is assumed that the stream geometry will be unstable.Either a change in the stream geometry or a milder slope ofthe stream will be needed to reduce the average velocity inthe stream within the allowable limit. This technique isnormally used to test the stability of an existing streamcross section rather than to design a conveyance channel.
The regime concept is one of the most widely usedmethods in open channel flow to design a stable alluvialchannel flowing on a mobile sandy bed. This concept wasinitially developed in India and was based on the data col-lected from stable channels in the Punjab region.
The original definition of the regime theory is given byLindley in 1919 (ASCE, 1963) as follows:
When an artificial canal is used to convey silty water,both bed and banks scour or fill, changing depth, gra-dient and width until a state of balance is obtained atwhich the channel is said to be in regime.
The regime type of equations proposed by various re-searchers relate average velocity with depth or hy-
draulic radius R and energy slope Se . Over the years the re-gime concept has been modified, better and more useful re-lationships have been developed, and presently the designengineer will usually use some type of regime equation todesign a conveyance channel flowing through alluvial ma-terials.
Kennedy (Lacy, 1958) proposed the following equationin 1895 which was based on his work with the regime typecanals in India.
(20)
where K ranges from 0.39 to 0.84 and m ranges from 0.52to 0.73. Then in 1919 Lindley (Lacy, 1958) proposedequations relating velocity ‚ depth ‚ and width W. From1919 to 1958 a number of researchers, such as Lacy, Bose,Malhotra, Blench, White, Inglis, Leliavsky, and others madesignificant contributions toward the understanding of theregime type of canals (ASCE, 1963; Simons and Richardson,1971). Lacy (1958) related wetted perimeter WP, hydraulicradius R, and slope S e to discharge Q and silt factor fs .
7
Blench (1969) in 1941 proposed a division of fs into bed-factor and side-factor to take into account the roughnesssand material variabilities between the side and the bed ofthe stream. Blench also replaced wetted perimeter and hy-draulic radius by width and depth of the channel.
Leopold and Maddock (1953) found that width, depth,and velocity of flow in rivers varied with mean annual dis-charge at any specified cross section. These parameterswere shown to increase in value in the downstream direc-tion. The relationships proposed by Leopold and Maddock(1953) are given by equations 21, 22, and 23.
(21)(22)(23)
Here a, b, c, i, j, and l are coefficients to be determinedfrom field observations. The mean values of the coef-ficients b, i, and l for a number of river basins in the UnitedStates are given by equation 24.
b = 0.5i = 0.4l = 0.1
(24)
On the basis of field data collected from noncohesiveand partly cohesive channels in India, Pakistan, and theUnited States, Simons and Albertson (1963) have proposeda set of regime type equations to determine the stable cross-sectional shape of an alluvial stream. The relationships pro-posed by Simons and Albertson are given below.
(25)(26)(27)(28)
Here, WP is the wetted perimeter in feet, R is the hydraulicradius in feet, A is the cross-sectional area in square feet,is the average velocity in fps, Q is the discharge in cfs, and Sis the slope. The relationships given by equations 25 through28 are valid for streams and canals with sand beds and co-hesive banks. Simons and Albertson also have given rela-tionships valid for streams flowing on a noncohesive bed
with noncohesive bank materials.Stall and Fok (1968) have developed hydraulic geometry
relationships for 18 river basins in Illinois. Their approach isbasically similar to that of Leopold and Maddock (1953).They have developed hydraulic geometry relationships withthe Horton-Strahler stream order (Stall and Fok, 1968) as aparameter. Their relationships should enable the designengineer to determine the hydraulic geometry parameters atany location in the river basin for a specified discharge ofknown frequency. Later, Stall and Yang (1970) showedthat the hydraulic geometry relationships are also valid for12 river basins located in the humid areas of the UnitedStates. A recent investigation by Bhowmik and Stall (1979)
has definitely shown that the hydraulic geometry relation-ships are also valid for the floodplains of the streams andrivers in the humid areas of the United States.
Maddock (1970) commented tha t the re la t ionshipsamong W, , , and S are not determinate unless the con-straints on the development of the bed form is known.When the rate of sediment transport in the stream is known,the indeterminate part between the hydraulic variables canto some extent be eliminated. However, the flow in a nat-ural channel is a complex phenomenon and no easy solu-tion exists. Still, with the research work already completedand the work that is now being conducted, the designengineer should be able to arrive at a technically sound de-sign of a conveyance channel flowing through alluvial ma-terials.
Flow around Bends
The mechanics of flow in a curved open channel hassome distinct characteristics that are absent in a straightchannel. The forces that the flow encounters not only aredifferent in nature, but also are very complex and not easilyunderstood. Some generalized comments and theoreticalequations can be developed for flows with Froude numbersequal to or less than 0.5. The regime of flow in naturalchannels is such that the numerical value of F is normallyless than 0.5. Leopold et al. (1960) analyzed the Froudenumber for 62 stream gaging stations around the UnitedStates. The values of F for bankfull discharges were foundto be less than 0.45 in 92 percent of the cases. Thus, anytheory or equation that is developed for flow in open chan-nels for F equal to or less than 0.5 should be valid for themajority of streams and rivers.
When the flow starts to enter a bend, the streamlinesbecome curved in plan because of the restraint exerted bythe stream banks. For potential flow, the shapes of thestreamlines can be determined by integrating Laplace’sequation. However, flow in natural channels never followspotential flow theory. The governing equations for openchannel flow can only be solved in conjunction with somesimplified assumptions.
In the following subsections some of the theories per-taining to the flow around a bend are described briefly.
Superelevation
As the flow moves around a bend, the streamlines arecurved, centrifugal forces are developed, and the transversewater surface profile becomes inclined with an increase ofwater depth near the outer bank and a consequent decreaseof water depth near the inside bank. The difference betweenthe water levels near the outside bank and the inside bankis called superelevation. The magnitude of superelevation is
8
normally high in case of rigid boundary channels where thegeometry of the channel remains the same in both thestraight and the curved reaches of the stream.
Investigators, such as Woodward (1920), Shukry (1950),Rozovskii (1957), Ippen and Drinker (1962), and manyothers, have worked on the development of theory and theanalysis of flow around bends. A number of analytical rela-tionships have already been developed to estimate the mag-nitude of the superelevation for a set of flow conditions.The basic equation for estimating the numerical value ofthe superelevation is equation 29.
(29)
Here Z is the superelevation, Vv is the average velocityin any vertical inside the bend, ri and ro are the inside andoutside radius of curvature of the bend, respectively, andr is the variable. In order to integrate equation 29, the dis-tribution of flow velocity across the width of the channelalong any radius in the bend must be known. Woodward(1920) assumed a constant transverse velocity distributionand obtained equation 30 to determine the superelevation.
(30)
In this case, is the average velocity in the cross section, Wis the top width, g is the acceleration due to gravity, and rcis the radius of curvature of the centerline of the bend.
When the transverse velocity distribution is approxi-mated by a free vortex pattern, the equation for super-elevation becomes (Shukry, 1950) as follows.
(31)
Ippen and Drinker (1962) assumed that the averagespecific head remains constant and that the high velocitiesoccur near the outer bank of the channel. For situationssimilar to this, a forced vortex pattern of velocity distribu-tion can approximate the transverse velocity distribution inthe bend. With these assumptions, equation 32 is obtainedfor estimating the superelevation.
(32)
When the transverse velocity distribution is approxi-mated by a combination of forced vortex for the inner halfof the width and free vortex for the outer half of the width,with the maximum average velocity in the vertical stayingclose to the centerline of the bend, equation 33 is obtainedfor computing the superelevation.
(33)
Equations 30 through 33 are some of the equations thatare used to compute the superelevation in an open channelbend .
Velocity Structure
The presence of the superelevation in the bend developsanother phenomenon called secondary circulation. Com-
bined effects of these factors change the velocity structureinside a bend. The core of high velocity flow is normallylocated near the center of the channel in a straight reach.But as the flow moves around the bend, a transverse in-clination of the free water surface will occur decreasingthe water depth near the inside bank at the entrance of thebend. This decrease in flow depth is associated with an in-crease in flow velocity at that location. However, as theflow proceeds downstream, the centrifugal force and theexchange of momentum between horizontal layers due totransverse circulation will change the velocity structure,and move the higher velocity filament near the outsidebank. This high velocity flow may stay close to the outsidebank for a considerable distance in the downstream direc-tion unless the stream again meanders and initiates anotherchange in the velocity structure.
Most of the researchers assumed the transverse velocitydistribution to follow a relation similar to the one givenby equation 34.
(34)
If m 1 equals +1, the velocity distribution is called a forcedvortex pattern and if m1 equals -1, the velocity distributionis called a free vortex pattern.
Rozovskii (1957) presented a detailed study of flowaround bends for an open channel with low Froude number(F < 0.15). He has presented a set of plots which can beused to determine transverse velocity distribution aroundan open channel bend. Rozovskii’s (1957) curves and plotsneeded for estimating the transverse velocity distribution atany cross section inside the bend are shown in figure 3. Thecross-sectional shape of the bend was assumed to be para-bolic and is given by equation 35 below.
(35)
Here, D max is the maximum depth, W is the top width, andX' is the distance of the individual vertical from the center-line of the stream. Dmax was assumed to occur at the center-line of the channel. The value of ∆ in figure 3a is to betaken in degrees. This is the numerical value of the includedangle at the center of the curve made by a line extendingfrom the cross section under consideration and a line ex-tending from the cross section at the beginning of thebend. In figure 3a, Vvm is the maximum average velocityat a vertical in the straight portion of the stream. It wasassumed that Vvm occurs at the centerline of the channel.The distribution of Vv is given by equation 36.
(36)
Here d is the depth of water at any individual vertical.
In order to calculate the transverse velocity distribu-tion at any cross section in a bend, the value of , is cal-culated by the equation shown in figure 3a. Here Dmaxis the depth of water at the centerline of the stream,C/(g) 1 / 2 is obtained from equation 14, and W and ∆
9
Figure 3. Dimensionless curves to determine transversevelocity distribution in a bend
are taken from the stream geometry data. Dependingupon the value of ∆ ', the transverse velocity distribu-tion is estimated from a curve or curves given in figure3a. However, figure 3b which is developed from figure 3acan also be used to estimate the transverse velocity distribu-tion in the bend.
Secondary CirculationSecondary circulation can be defined as a pattern of cir-
culation that will develop in an open channel mainly be-cause of the presence of curves in its alignment. Themechanics of initiation of the secondary circulation can be
explained by considering the transverse inclination of thewater surface and the centrifugal force that is exerted onthe water particles as the water moves around a bend.
If we divide both sides of equation 30 by W, the trans-verse inclination of the water surface designated as I r be-comes independent of the width of the stream as follows.
(37)
This shows that the inclination of the water surface or thetransverse slope of the water surface in a bend is a functionof the flow velocity, radius of curvature, and the accelera-tion due to gravity.
10
For uniform flow in a prismatic channel, the So , S w,and S e on figure 1 should be parallel, that is, Se /S w =S w/S o = 1. But whenever Se/S w > 1, the energy dissipationis greater than uniform flow and an accelerating flow is im-plied. When Se /Sw < 1, the energy dissipation is less thanuniform flow, the depth of flow increases, and a conversionof kinetic energy to potential energy takes place. Thus, aplot of Se /Sw or S e/S o can shed some light as to the rateof energy dissipation in an open channel.
Bed Topography
The presence of the secondary circulation and the lateralmovement of the high velocity flow toward the outsidebank of the bend will erode the bed and the bank of thechannel if they lack protection. The magnitude of scour willvary depending upon many physical factors. As the watermoves around a bend with erodible bed and bank, thesecondary circulation increases, exchange of momentum ac-celerates, the high velocity flow moves gradually toward theoutside bank, and a gradual change in the bed topographytakes place. The trapezoidal or symmetrical parabolic crosssection that may be present at the beginning of the bend,may for all practical purposes be transformed into a skewedcross section. The maximum depth is usually located nearthe outside bank and sediment will be deposited near theinside bank forming the so called ‘point bars.’ A knowledgeof the variability of cross-sectional shapes in any open chan-nel bend is needed to investigate the dispersion of materialsand the hydraulics of natural streams.
Researchers such as Yen (1970), Engelund (1974),Bridge (1976), Gottlieb (1976), and others have developedempirical relationships to estimate the bed topography inan open channel bend.
Pools and Riffles
Natural streams and rivers flow through a series of poolsand riffles during low stages. During high stages, when theriver is full from flood flows, the pools and riffles are usual-ly suppressed, the longitudinal water surface profile be-comes smooth, and the variability in the flow due to thepresence of pools and riffles disappears.
The change in the flow regime of a river from the pooland riffle sequence to a regime with high stages is a normaloccurrence in a stream located just downstream of a con-trolled man-made reservoir. The operation and managementof the reservoir may require different quantities of water tobe released within a period of a couple of days. Thus astream which is flowing through a series of pools and rifflesduring low releases, may carry bankfull discharge within aperiod of two weeks. Therefore, it is essential that the lowflow dynamics of streams and rivers be studied.
pressure force is generated by the differential increase in
from the axis of the
(38)
Because of the presence of frictional resistance at thebed and sides of the channel, the velocities along any verti-cal in a bend vary from a maximum value at or near thewater surface to a minimum value at the bottom. The flowvelocity near the water surface will consequently be morethan the average velocity in the respective verticals. Thecentrifugal force Cf is a function of the square of theflow velocity. In order to maintain the balance of theforces, the centrifugal force, which is trying to push thewater particles away from the stream in a radial direction,must be counterbalanced by the pressure force ∆P. The
water depths as a result of the superelevation. Depth-in-tegrated values of Cf and ∆ P are equal. However, near thewater surface where the flow velocity is greater than theaverage velocity, Cf is greater than ∆ P. Similarly, near thebed of the stream, the flow is less than the average velocityand consequently ∆ P is greater than Cf. At the point wherethe water is flowing with an average velocity, ∆P equals Cf.This differential between the ∆ P and Cf will displace thewater particles away from the centerline near the water sur-face. A similar displacement near the bed of the stream to-ward the inner side of the bend will take place.
As a result of this opposite radial displacement of thewater particles, a helicoidal motion will develop in a bendin addition to the normal longitudinal flow. This helicoidalmotion is termed the secondary circulation in a bend.
The secondary circulation in the bend will have a verticalvelocity component directed downward on the outside
bank of the bend. This vertical component of the velocitywill help to dislodge the bank materials from the outsidebank and will contribute to the instability of the outsidebank. The resultant of this vertical velocity componentand the normal flow velocity vector at or near the outsidebank will be deflected by an anglechannel. Rozovskii (1957) reported the following equationf o r based on field observations.
Prus-Chacinski (1966) indicated that equation 38 should beapplicable for natural and laboratory channels.
Energy Dissipation
Changes in the flow structure in a bend lengthen thepath of motion of an individual particle for its journey a-round the bend. Exchange of momentum between separatelayers of flow is increased, which in turn increases the dis-sipation of mechanical energy. Ippen and Drinker (1962)found that the rate of energy dissipation is maximum at theend of the bend. This rate of energy dissipation was ex-pressed by them as a ratio of energy slope at the end of thebend to that at the beginning or at the entrance section ofthe bend.
11
Keller (1978) has indicated that the maintenance ofpools and riffles is very important in any channelizationproject. Pools and riffles help not only to maintain an ade-quate aquatic life in the stream ecosystem by creating al-ternatively deep and shallow waters, but also to dissipatethe excess energy and maintain a stable flow regime. Chan-nelization projects where pools and riffles are artificiallycreated to maintain a better balance of the stream eco-system are better than a straight and lined canal.
Stall and Yang (1972) have analyzed the hydraulicgeometry of pools and riffles for a 53-mile segment of
the Kaskaskia River. From their analysis, it was concludedthat the length of the pools can be expected to be about 8times longer than the length of the riffles.
Keller (1978) has noted that the geometric patternsof the pools and riffles remains unaltered during and afterthe passage of high magnitude floods. However, changes inthe land use pattern, upstream construction, and bankfailures will change drastically the pattern and the locationof the pools and riffles in a natural channel or in an arti-ficial one.
DATA COLLECTION
Data used in this research project were collected fromtwo reaches of the Kaskaskia River. Figure 4 shows theKaskaskia River drainage basin and the locations of thereaches selected for study. The total drainage area of theriver is 5801 square miles. The drainage area at Reach 1 is1330 square miles and that at Reach 2 is 2720 square miles.Each reach is located downstream of a man-made lake.Reach 1 is located about 12 miles downstream of LakeShelbyville and Reach 2 is located about 7 miles down-stream of Carlyle Lake.
These reaches were selected downstream of the man-made lakes to take advantage of the relatively steady flowthat exists below such lakes. The flow in a natural river isnever constant, and usually will be unsteady and nonuni-form. Short-term prediction of the flow is very difficult.Collecting a precise set of hydraulic data from a segment ofa river 2 to 3 miles long requires at least 1 week. In naturalstreams and rivers, the flow normally changes from day today. This is especially true during flood stages. But if theflow in a river is controlled by the release rates from areservoir just upstream of the reach under investigation,then it is possible to keep the rates of flow relatively steadyfor a short period of time even during flood stages. Keepingthe flow steady for such a short period of time should notadversely affect the regime of the river. As a matter of fact,both lakes shown in figure 4 are operated by the U.S. ArmyCorps of Engineers for flood protection and recreationaluses. Thus it is a normal operational procedure to releasethe water from the lakes at a constant rate extending for aperiod of a few days, which was an advantage during thedata collection phase of this investigation.
Hydraulic Geometry of the ReachesThe preliminary selection of the reaches was made from
the plan view of the river as shown on U.S. GeologicalSurvey quadrangle maps. Easy access to the sites, existence
of a wide variety of bends and straight segments in thereaches, closeness to the reservoirs, and the availability ofsupport personnel were some of the factors considered inthe selection process. A field trip was made to each-reach tomake sure that these sites satisfied all the initial require-ments.
After the final selections were made, the approximatelocation of the cross sections, the starting points for bothreaches, and the total length of the river to be investigatedwere marked on individual quadrangle maps. Two privatesurveying firms were contracted to perform the necessarysurveying work. The surveyors were asked to determine thecross-sectional elevations of the river at about 15 to 17well-placed cross sections in each reach. They were also re-quired to develop the plan view of each reach. Permanentconcrete surveying monuments were installed on both sidesof the river at each of the selected cross sections. The exactposition of the monuments related to Illinois State PlaneCoordinates and their elevations above mean sea level werealso determined. These permanent concrete monumentswere used as bench marks in all subsequent data collectiontr ips .
Figure 5 shows the aerial view of Reach 1 below LakeShelbyville. This photograph was taken on November 13,1975. The plan view of the reach, the location of the crosssections, and the location of the monuments are given infigure 6. The geometric characteristics of this reach aregiven in table 1. Here, the exact location of each section,the beginning and end of each bend, the deflection angleand the radius of curvature of the bends, the top widthsat each section, and the ratio rc/W are given. The plan viewof Reach 2 is shown in figure 7, and the geometric prop-erties of this reach are given in table 2.
In Reach 1 (figure 6) there are at least four sharp bends.The beginning and the lower part of the reach are basicallystraight. Whereas for Reach 2 (figure 7), there are threesharp bends and a long straight segment near the lower
12
Figure 4. Drainage basin of the Kaskaskia River and locations of the test reaches
13
Figure 5. Aerial view of Reach 1
14
Figure 6. Plan view of Reach 1
part of the reach. Both reaches of the river have a goodcombination of straight reaches and bends affording a widevariety of conditions in the study of the hydraulics offlow in an open channel.
Velocity Distribution and Water Surface Profiles
Once the initial surveying was completed, a field crewwas assembled to collect the basic data. The crew consistedof one or two engineers, two surveyors, and two technicians.One of the technicians was from the U.S. Geological Surveyand helped to collect the velocity distribution data with aPrice Current Meter following the standard procedure ofthe U.S. Geological Survey.
Figure 8 shows a photograph of the actual data col-lection arrangement. A marked steel tag line was stretchedacross the river to align the boat and also to move it acrossthe river. The procedures followed in data collection wereas follows:
1 ) Organize the field crew so that they are ready to go tothe field with short notice.
2 ) Request the U.S. Army Corps of Engineers to keepthe release rates constant for a time period sufficientto collect the data when the runoff condition in thewatershed was such that the release rates from thereservoir would be within the specified requirement.
3) Start collecting the data preferably on Monday, begin-ning at cross section 1 in each reach (figures 6 and 7).
15
16
Table 1. Geometric Charateristics of Reach 1
Distance alongthe centerline
(ft)
Total deflection angleor central angle ofbend, ∆ (degrees)
Centerline radiusof curvature,
rc (ft)Top width,
W (ft) rc /W Remarks0 Thompson Mill Covered Bridge
510 38 990 Beginning of Bend 1680 38 990 125 7.92 Cross section 1
1090 38 990 End of Bend 11550 55 980 Beginning of Bend 21980 55 980 129 7.60 Cross section 22380 55 980 169 5.80 Cross section 32490 55 980 End of Bend 22490 84 448 Beginning of Bend 32743 84 448 133 3.37 Cross section 43160 84 448 End of Bend 33520 140 134 Beginning of Bend 43759 140 134 119 1.13 Cross section 53860 140 134 End of Bend 44207 136 Cross section 64700 148 102 Beginning of Bend 54955 148 102 119 0.86 Cross section 74980 148 102 End of Bend 55407 126 Cross section 85830 158 96 Beginning of Bend 65959 158 96 143 0.67 Cross section 96120 158 96 End of Bend 66379 174 Cross section 106840 134 114 Beginning of Bend 76999 134 114 166 0.69 Cross section 117130 134 114 End of Bend 77971 155 Cross section 128100 93 160 Beginning of Bend 88291 93 160 113 1.42 Cross section 138380 93 160 End of Bend 88603 148 Cross section 149155 108 Cross section 15
10603 141 Cross section 1611739 120 Cross section 17
4) Collect point velocities at about 5 to 6 points in eachvertical and for 20 to 25 verticals in each cross sec-tion. Use boat and standard gaging equipment to col-lect the velocity data.
5) Measure the water surface elevations twice a day onboth sides of the river at each cross section with thepermanent concrete monuments as bench marks.
6) Repeat the same procedure the following day andcontinue until velocity distribution data have beencollected from all cross sections in each reach.
A crew of three to four persons was needed to collectthe velocity data and two other persons were needed tomeasure the water surface profiles. Measuring the velocitydistribution data at each cross section required about 2hours.
To measure the water surface profiles, the surveyor useda level, a level rod, and the permanent concrete monumentsinstalled on the bank of the river. Figure 9 shows twophotographs of the technique used in the field. The sur-veyor initially took a level reading on the monument (figure9a) and then another level reading at the water edge (figure9b). A 24-inch rod with a flat plate welded at one end washand driven into the soft bank near the water edge makingsure that the water surface and the top of the flat platewere at the same level. This flat surface was used as the plat-form to measure the water surface elevation with the aid ofthe level rod and the level. With the relative elevation ofthe water surface with respect to the nearest monument,the water surface profile along the whole length of thereach was easily determined. The data are given in the Ap-pendix.
Figure 7. Plan view of Reach 2
Bed and Bank Material SamplesOne of the most important physical parameters in an
open channel that directly affects the resistance to flow isthe nature and distribution of the bed and bank materials.During periods of low flow, three field trips were made togather the bed and bank material samples from both reaches.
Two different sets of bed and bank material sampleswere collected. The first set consisted of bed materials col-lected from the middle of the river at or near each cross sec-tion (figures 6 and 7). An Ekman dredge and/or a shoveland a scoop were the only equipment needed to collect thesamples. In all 28 bed material samples were collected fromthe two reaches.
The second set was a special one of bed and bank ma-terial samples from two sequences of riffles and pools lo-cated in Reach 1. The first sequence of riffle-pool-riffle ex-tended from about 200 feet upstream of the ThompsonMill Bridge to within 300 feet of cross section 2. Thesecond pool-riffle-pool sequence extended from cross sec-
tion 13 to cross section 15. There were other pool and rif-fle sequences in the two reaches. The two sequences se-lected for this investigation appeared to have a number ofvariables which could afford an opportunity to study thelow flow hydraulics in a natural river.
Altogether, 51 bed and bank material samples were col-lected from these two pool and riffle sequences. Thesesamples were collected during low flows when 60 to 70 per-cent of the bed was dry. Most of the samples were from thebed of the river. Normally three samples were collectedfrom each cross section, one from the center of the riverand the other two from each side close to the toe of thebanks. Before collecting a sample, the location of the sitewas selected by visual inspection. The exact position of thesite with respect to the ground stations was then determinedby using theodolite and stadia measurements. Before col-lecting the samples, a 2- by 2-foot frame with grid pointsat 0- to 1-foot intervals was placed on top of the site, and aphotograph was taken. Figure 10 shows such a photograph
17
18
Table 2. Geometric Characteristics of Reach 2
Distance along the centerline
(ft)
Total deflection angle or central angle of bend, (degrees)
Centerline radius of curvature,
rc (ft) Top width,
W (ft) rc /W Remarks 0 73 1460 159 9.18 Cross section 1
1200 73 1460 157 9.30 Cross section 2 1660 73 1460 End of Bend 1 1680 75.5 1248 Beginning of Bend 2 2100 75.5 1248 161 7.75 Cross section 3 2760 75.5 1248 171 7.30 Cross section 4 3260 75.5 1248 146 8.55 Cross section 5 3340 75.5 1248 End of Bend 2 3580 183 300 Beginning of Bend 3 3940 183 300 151 1.99 Cross section 6 4222 183 300 158 1.90 Cross section 7 4560 183 300 End of Bend 3 4790 168 Cross section 8 6450 188 Cross section 10 7650 182 Cross section 11 8640 106 700 Beginning of Bend 4 8978 106 700 149 4.70 Cross section 12 9860 106 700 End of Bend 4
12274 188 Cross section 14 14644 199 Cross section 15
Figure 8. Velocity data collection
∆
Figure 9. Water surface elevation determination
19
Figure 10. An undisturbed bed material sample
of an undisturbed bed material sampling site. Subsequently,the top layer of the bed material was scraped, bagged, andbrought to the laboratory for particle size analysis.
In general, the banks of the river were stable. In someinstances, however, the banks were eroding at a steady
rate. This was especially true near the outside of the bends.Figure 11a shows the outside bank of the river near crosssection 12 (figure 6). The bank erosion at this location isquite vivid. Figure 11b shows the river near cross section4, Reach 2 (figure 7), looking in the upstream direction.
ANALYSIS AND RESULTS
The results of this research are presented under a num-ber of different headings. This separation of the researchresults was made in order to be able to discuss the variousaspects of flow dynamics in a concise and precise manner.Part of the results of this research has already been pre-sented by Bhowmik and Stall (1978a, 1978b) at twonational technical society meetings.
Geomorphology
Physiographically, the Kaskaskia River is located in theglaciated portion of the state of Illinois. The two physio-graphic divisions through which the river flows are theBloomington Ridged Plain and the Springfield Plain(Leighton et al., 1948). The drainage pattern in the Bloom-ington Ridged Plain is in the initial stages of development,whereas the drainage patterns in the Springfield Plain areall well developed.
The reaches selected for the present study are located inthe Springfield Plain. Reach 1 is located near the upper endof the plain and Reach 2 is located near its lower end.Geomorphologically, the development of a river basin canbe tested by analyzing the partial drainage areas of the riverwith reference to the respective fall or elevations of themain stem of the river at different locations. Figure 12shows such a plot for the Kaskaskia River. This type of plotis called either an area-altitude curve or a hypsometric curve.Here, the ratio of the drop of any specified elevation fromthe highest point in the drainage divide to the total drop ofthe river is plotted against the ratio of the horizontal areaabove the respective elevations to the total drainage area ofthe river. The shape of this curve will vary depending uponthe geologic age and the developmental pattern of the river.The shape of the hypsometric curve for the Kaskaskia Riverindicates that the river has passed through the young stagesand is presently in an equilibrium or mature stage of devel-opment. The approximate locations of the two reaches arealso shown in this figure.
20
Figure 11. Examples of bank erosion: (a) outside bank near cross section 12, Reach 1 and(b) near cross section 4, Reach 2
21
Figure 12. Area-altitude or hypsometric curve for Kaskaskia River
Figure 13 shows the profile of the main stem of the The other parameter shown in table 3 is called theKaskaskia River. The approximate location of both study uniformity coefficient U, and is defined by the ratio givenreaches is also given here. in equation 40.
U = d 60 /d10 (40)
Bed Material Sizes The numerical values of σ and U indicate a measure of thegradation of the particles. Higher values of σ and U will in-
It has already been mentioned that a total of 28 bed ma- dicate a very well graded material, whereas a lower value ofterial samples was collected from the two reaches. These σ and U will demonstrate the uniformity of the particles.samples were analyzed to determine the particle size dis- The last column in the table shows the general nature of thetribution. Figure 14 shows a typical plot of the particle bed materials. In order to determine if the bed materials forsize distribution curve for sample No. 8 from Reach 1 different samples are similar or not, frequency analyses for(figure 6). Similar plots were developed for the other 27 dsamples. Table 3 shows some of the parameters that were
50 and d95 sizes were made, as shown in figures 15 and 16.Figure 15 shows that 12 out of 16 samples from Reach 1
determined on the basis of the analysis of particle size of have d sizes smaller than 0.42 mm with the lowest value50the bed materials. The d and d indicate the equivalent50 95 at 0.011 mm (table 3). Basically all these particles areparticle diameters for which 50 percent and 95 percent, medium to fine sand. For Reach 2 (figure 15) there is somerespectively, of the particles are finer in diameter. The variability in the d sizes, but they are also sandy. Thestandard deviation, σ, is defined by equation 39.
50
variability of the median diameters for this reach may have
( 3 9 ) been the result of the sampling of the particles either frompools or riffles. This variability is not the same as the gener-
Here d 8 4 . 1 and d15.9 indicate the equivalent particle diam- alized changes that occur in any segment of a river becauseeters for which 84.1 percent and 15.9 percent, respectively, of its relative position with respect to the total length ofof the particles are finer in diameter. the river. The bed materials did not indicate the presence
22
Figure 13. Profile of the Kaskaskia River
of any overall trend for either increasing or decreasing sizefrom upstream to downstream.
The frequency distributions of the d 95 sizes from bothreaches (figure 16) indicate that even the largest sizes frommost of the samples are less than about 1.6 to 1.9 mm. Thiswill put most of these particles in the sandy category.
The σ and U values from table 3 indicate that the bedmaterials from both test reaches are basically well gradedmaterials.
Hydraulic and GeometricCharacteristics of the Reaches
Hydraulic and geometric parameters that were eithermeasured or computed from the data collected from thefield are shown in tables 4 (Reach 1) and 5 (Reach 2). Dataare shown for low, medium, and high flows for bothreaches. The date of data collection, computed discharge Qin cubic feet per second based on measured velocity data,cross-sectional area A in square feet, average velocity i nfeet per second, average depth in feet, and hydraulicradius R in feet are the parameters given.
There was some variability in the measured discharges onthe same day at various cross sections because of the changesin the upstream flow rates and the changes in the local in-flows. Rather than using an average discharge for all thecross sections based on the measured values of Q at dif-ferent cross sections for the same day, the measured valueof Q at each cross section was used for further analysis.
The cross-sectional shape of the river, a basic hydraulicgeometric characteristic, was further analyzed. The cross-sectional shapes in a natural river with erodible bed andbanks are neither rectangular, trapezoidal, nor parabolic inshape, Flow hydraulics, bed and bank materials, snags, andhuman alterations determine the stream’s cross-sectionalshape. Rozovskii (1957) assumed a parabolic distribution.Other researchers tried to fit either empirical or theoreticalshapes based on assumed patterns of secondary circulationor combinations of different dynamic forces, especiallyin a bend.
Figure 17 shows the nondimensional plots of the cross-sectional shapes for straight reaches and bends from Reach1. A theoretical curve after Rozovskii (1957) is also shown.It appears that in the straight reaches, if about 55 to 60 per-
23
24
25
Table 3. Particle Size Characteristics of the Bed Materials, Reaches 1 and 2
Sample number d50 (mm) d95 (mm) U Remarks Reach 1
1 0.22 0.28 1.41 3.14 Sand 2 0.56 11.0 4.30 3.30 Sand 3 0.37 0.88 1.64 2.35 Sand 4 0.046 0.20 4.50 16.05 Silty loam 5 0.089 0.33 8.42 42.86 Sandy loam 6 0.34 0.70 1.46 2.00 Sand 7 0.84 16.0 6.70 4.48 Sand 8 0.63 4.5 2.44 3.13 Sand 9 0.30 0.94 1.35 1.55 Sand
10 0.023 0.19 Silty loam 11 0.38 0.77 1.40 1.71 Sand 12 0.011 0.047 Silty clay loam 13 2.1 12.0 3.60 7.78 Sand 14 0.37 0.70 1.32 1.58 Sand 15 0.32 1.4 1.76 1.80 Sand 16 0.16 3.3 5.21 6.25 Sand
Reach 2 17 0.036 0.27 Silty loam 18 0.0048 0.058 Silty clay 19 0.39 1.0 1.60 6.00 Sand 20 0.75 19.0 10.67 15.42 Sand 21 0.28 0.51 1.20 1.47 Sand 22 0.31 0.64 1.25 1.50 Sand 23 0.18 0.29 11.72 Sandy loam 24 0.85 4.1 4.01 24.44 Sand 25 0.32 0.61 1.28 1.62 Sand 26 0.48 4.7 2.80 2.95 Sand 27 0.31 5.0 3.19 2.44 Sand 28 0.22 0.59 2.17 10.45 Sand
Figure 15. Frequency distribution of d50 sizes of the bed materials
σ
Figure 16. Frequency distribution of d sizes of the bed materials95
Figure 17. Cross-sectional shapes at Reach 1
26
27
Table 4. Hydraulic Characteristics of Reach 1
Cross- section number
Date of collection
Discharge Q (cfs),
Area, A
(sq ft)
Velocity, (fps)
Depth, D (ft)
Hydraulic radius, R (ft)
Low Flow - Collected 1975 1 10/20 1106 629.0 1.76 6.48 6.17 2 10/20 1058 649.0 1.63 5.69 5.45 3 10/21 1125 623.0 1.81 5.72 5.56 4 10/21 1159 622.0 1.86 5.76 5.55 5 10/21 1177 560.0 2.09 6.15 5.71 6 10/21 1170 680.0 1.72 5.67 5.48 7 10/22 1030 605.0 1.70 7.12 6.51 8 10/22 989 563.0 1.76 5.52 5.36 9 10/22 1171 1173.0 1.00 9.24 8.56
10 10/22 900 541.0 1.60 4.96 4.36 11 10/22 953 518.0 1.84 4.39 4.05 12 10/23 984 534.0 1.84 5.18 5.04 13 10/23 933 512.0 1.82 5.82 5.39 14 10/23 945 544.0 1.74 4.57 4.46 15 10/23 954 481.0 1.98 5.12 4.91 16 10/24 950 575.0 1.65 5.13 4.96 17 10/24 939 650.0 1.97 7.30 6.19
Medium Flow - Collected 1977 1 5/11 1423 817.5 1.74 8.09 7.57 2 5/11 1363 726.3 1.79 6.32 6.10 3 5/11 1378 725.0 1.90 6.47 6.20 4 5/11 1419 773.8 1.83 7.16 6.85 5 5/11 1469 746.3 1.97 7.94 7.31 7 5/12 1495 896.3 1.67 9.34 9.14 8 5/12 1399 712.5 1.96 6.36 6.20 9 5/12 1530 903.8 1.69 8.69 8.07
10 5/13 1391 712.5 1.95 5.24 5.13 11 5/13 1436 775.0 1.85 5.96 5.66 12 5/13 1406 698.8 2.01 6.41 6.19 13 5/13 1454 640.0 2.27 6.53 6.10 14 5/16 1338 687.5 1.95 5.46 5.33 15 5/16 1453 716.3 2.03 7.02 6.57
17 5/16 1401 785.0 1.79 8.01 7.20
High Flow - Collected 1978 1 3/20 4555 1657.9 2.75 12.37 11.51 2 3/20 4643 1646.7 2.82 11.20 10.56 3 3/20 4674 1830.6 2.55 12.37 11.81 4 3/21 4620 1682.8 2.75 13.15 5 3/22 3831 1475.9 2.60 12.61 11.46 6 3/21 3366 1668.2 2.02 12.0 10.76 7 3/22 3556 1610.4 2.21 14.25 8 3/22 3375 1493.9 2.26 10.83 10.16
10 3/23 3532 1694.1 2.09 9.85 9.46 11 3/23 3405 1629.7 2.09 9.88 9.48
–
28
Table 5. Hydraulic Characteristics of Reach 2
Cross section number
Date of collection
Discharge, Q (cfs)
Area, A (sq ft)
Velocity, (fps)
Depth, D (ft)
Hydraulic radius, R (ft)
Low Flow - Collected 1977 1 5/17 285 243.8 1.17 1.97 1.94 2 5/17 287 217.5 1.32 2.05 2.02 3 5/17 291 253.8 1.15 2.64 2.59 4 5/17 277 188.8 1.47 2.01 1.97 5 5/17 284 333.8 0.85 3.93 3.80 6 5/18 305 448.8 0.68 4.93 4.78 7 5/17 289 430.0 0.67 5.18 4.94 8 5/18 277 268.75 1.03 2.86 2.80
10 5/18 296 353.8 0.84 3.43 3.34 11 5/19 286 407.5 0.70 4.25 4.12 14 5/19 286 387.5 0.74 3.84 3.77 15 5/19 283 400.0 0.71 3.31 3.23
Medium Flow – Collected 1975 1 12/8 2143 1136.2 1.95 7.95 7.81 2 12/11 2210 971.3 2.26 7.96 7.46 3 12/11 2200 1047.8 2.12 8.45 8.06 4 12/11 2228 1127.3 1.98 8.05 7.81 5 12/9 2169 1141.7 1.76 8.04 8.37 6 12/9 2112 1185.7 1.78 9.34 8.83 7 12/9 2161 1052.3 1.97 8.63 8.22 8 12/9 1583 934.1 1.76 6.77 8.04
11 12/10 2288 1983.2 2.03 8.27 8.02 12 12/10 2025 993.9 2.08 9.04 8.82 14 12/10 2183 1254.9 1.71 9.65 9.53 15 12/10 2165 1409.9 1.53 10.0 9.52
Higb Flow - Collected 1977 1 12/13 3999 1738.9 2.30 11.15 10.48 2 12/13 4013 1491.3 2.69 10.36 9.75 3 12/13 4027 1594.0 2.52 11.81 9.72 4 12/13 3810 1618.3 2.35 10.05 9.30 5 12/14 4013 2001.3 2.01 11.70 11.24 6 12/14 3799 1832.4 2.07 11.90 10.97 7 12/14 3680 1849.5 1.99 12.25 11.21 8 12/14 3573 1783.3 2.00 10.49 9.96
10 12/15 3460 1785.9 1.94 11.20 8.12 11 12/15 3297 1790.1 1.84 12.79 12.01 12 12/15 3461 1731.7 2.00 12.11 11.47 14 12/15 3388 1937.9 1.75 12.46 11.89 15 12/16 3442 2149.6 1.60 13.52 12.80
–
Figure 18. Flow duration curves for Reaches 1 and 2
cent of the bed is assumed to be level, the two natural sideslopes can be approximated by Rozovskii’s relationship.
However, the shape of the section is very close to trape-zoidal rather than parabolic. Furthermore, in bends thecross-sectional shape is definitely skewed, with maximumdepths occurring near the outside of the bend. The maxi-mum depths varied anywhere from 30 to 90 percent morethan the average depths. But the relative magnitudes of the
depths near the center of the cross sections for both thestraight reaches and bends remained at about 20 percentmore than the average depth in the cross section.
This pattern of bed topography may indicate that thelateral shape of the bed in a bend changes about a fulcrumnear the centerline. For similar flow and composition of
bed materials, the increase in maximum depth near the out-side of the bend is associated with a corresponding decreasein depth near the inside of the bend, and this increase anddecrease is to some extent proportional to the sharpness ofthe bend as expressed by the central angle of the bend.Similar types of variability were also observed for Reach 2.
Flow Frequencies
Altogether, seven sets of velocity distribution data werecollected from the two reaches. Out of the seven, four setswere collected from Reach 1 and three sets from Reach 2.
Figure 18 shows two flow duration curves for theKaskaskia River. Both duration curves were developed for
29
Table 6. Measured Average Discharges and Flow Frequencies for Reaches 1 and 2
Reach Date of Measured averagenumber collection discharge (cfs)
1 7/7/77 581 10/20/75 - 10/24/75 10401 5/11/77 - 5/16/77 14201 3/20/78 - 3/23/78 4000
2 5/17/77 - 5/19/77 2902 12/8/75 - 12/11/75 21602 12/12/77 - 12/16/77 3700
discharges occurring after the construction of the dams atShelbyville and Carlyle (figure 4). One of the curves wasdeveloped for discharges below Lake Shelbyville at theU.S. Geological Survey Cowden gaging station just down-stream of Reach 1. The other duration curve is for flowsjust downstream of Carlyle Lake. This duration curveshould give a good indication of the variability of the flowat Reach 2. Table 6 shows the flow frequencies and thecorresponding average discharges that were measured duringthe seven data collection trips. As indicated, a wide varietyof flow frequencies were covered in the collection of thesefield data.
For Reach 1, data related to the riffle and pool sequences
were collected at the flow of 58 cfs. Detailed water surfaceprofile and velocity data were collected for all other dis-charges. In this respect, the low, medium, and high flowsfor Reach 1 will correspond to the discharge of 1040, 1420,and 4000 cfs, respectively. Similarly for Reach 2, the low,medium, and high flows will correspond to the flows of290, 2160, and 3700 cfs, respectively.
Water Surface Profiles
Water surface profiles were measured daily on bothsides of the river at each cross section during each data col-lection period. Although the release rates from the reser-voirs were kept approximately constant, on occasion thedischarge changed because of local inflow, with a corre-sponding change in the water surface elevations. Normallythese changes were minimum except during the 1975 trip inReach 1 (table 4) where a sudden change in the lake levelforced a consequent change in the release rates below LakeShelbyville.
During high release rates from both lakes, water surfaceelevations fluctuated from day to day. These fluctuationswere not only because of the changed release rates, butalso because of flooding conditions in the surroundingareas and the influence of the local inflows into the testreaches.
Figures 19 and 20 show the centerline bed profile, thalwegprofile, and water surface profiles for low, medium, and
Flow frequencyin percent oftime exceeded
8 85 04 2
5
7 44 02 4
high flow conditions for Reaches 1 and 2, respectively.Cross-sectional data supplied by the surveying crew wereused to determine the thalweg and centerline profiles of thebeds of the river. In Reach 1 (figure 19) the thalweg andthe centerline profiles indicate that the river is flowingthrough a series of riffles and pools during low flow periods.Similar variability exists to some extent for Reach 2 (figure2 0 ) .
The water surface profiles plotted in figures 19 and 20for three flow conditions show the average water surfaceelevations at each cross section for a single day during thedata collection period. Although there were some minorchanges in the water surface elevations from day to day foreach data collection trip, the overall patterns for low,medium, and high flows remained identical.
It is interesting to note that the shapes of the water sur-face profiles for low, medium, and high flows for eachreach remained almost the same. During high flows, theriver was flowing at or above the bankfull stages at bothreaches, whereas for medium and low flows, the dischargeswere confined within the banks. This may indicate that al-though the flow conditions in a river may change over theyears, some hydraulic parameters such as the shape of thewater surface profile may not show any drastic changes.
In Reach 2, there is a rock ledge near cross section 13(figure 7). This rock ledge appeared to have acted as acontrol in the river and exerted its effects on the water sur-face profile even during the bankfull stages (figure 20).Naturally the effect of the rock ledge is more during lowflows than during the flooding season. For Reach 1, thedrop in water surface profiles remains more or less uniformexcept near the lower part of the reach where the river isbasically straight. Some local changes in the water surfaceprofiles resulted from constraints exerted by local ob-structions such as snags and trees.
Velocity Distributions
Vertical Velocity Distribution
The velocity distribution in any vertical changes withthe changing characteristics of the turbulence intensity of
30
Figure 19. Bed elevation and water surface profiles for Reach 1
31
Figure 20. Bed elevation and water surface profiles for Reach 2
the point velocities. However, on the average a general dis-tribution does exist and it can be expressed by an equationsimilar to the ones given in equations 5 through 8. Figure 21shows some typical plots of vertical velocity distributionsfrom Reach 2, cross section 15 (figure 7) for high flows.In general, on a semi-logarithmic paper the vertical velocitydistribution plots as a straight line indicating the validity ofequation 5 for open channel flows at least in the straightportion of the river.
It was previously mentioned that the d 85 or d 95 sizesof the bed materials can replace the effective roughnessheight in equation 5. Table 3 and figures 15 and 16 showthat the bed materials of the river at these two reaches con-sist mainly of sand. Thus the presence of bed forms (figure2) in the river cannot be ruled out.
Some of the vertical velocity distribution data from thestraight reaches were plotted on semi-log paper as log(y/d95)
versus v/V *. These points plotted approximately as astraight line (figure 22) and a best fitted equation was de-veloped as follows.
v/V * = 4.65 log(y/d 9 5 ) + 3.35 (41)
This equation is similar to equation 7 proposed by Leopoldet al. (1964) with d84 as the roughness element.
Average Velocity in the Individual Verticals
The velocity distribution data used for this research werecollected at 5 to 6 points in each vertical. However, it is astandard practice of the U.S. Geological Survey to measurevelocities at 0.2 and 0.8 depths in verticals more than 2 feetdeep and to take an average of these two values to computethei average velocity in the vertical. For verticals less than 2feet deep, normally one measurement is taken at the 0.6
32
Figure 21. Typical vertical velocity distributions(distances shown are from the right side of the river)
33
Figure 22. Nondimensional vertical velocity distribution plot
depth and this velocity is assumed to be the average velocityin the vertical.
In order to determine how the average velocities com-puted from 2 or 1 point measurements relate with thedepth-integrated average velocities determined from 5 to 6point measurements, the average velocities determined bythese two methods were compared. Figure 23 shows thecomparison between the average velocities for straightreaches. The abcissa shows the average velocities deter-mined by planimetering the area under the velocity distribu-tion plot on coordinate paper and determining the ratio ofthis area to the corresponding depth in the vertical. For aperfect agreement, all the plotted points should have fallenon a 45 degree line. In general, the average velocities com-puted from 0.2 and 0.8 depth measurements predicted thevelocities by 5 to 7 percent more than the realistic averagevelocity in each vertical.
A similar plot was also developed for bends and is givenin figure 24. Here also, the average velocities determinedfrom 0.2 and 0.8 depth measurements averaged about 5 to7 percent higher than the average velocities determined
from 5 to 6 point measurements. These two plots show thatin some instances, the discharge at a section in a river de-termined from 0.2 and 0.8 depth measurements may pre-dict the total flow of the river by 5 to 7 percent more thanthe flow determined from the detailed velocity distributiondata.
Average Velocity and Bottom Velocity
In all subsequent analyses, the average velocities used inthis report are the velocities that were determined from thedepth-integrated velocity distribution plots. The stabilityanalysis of open channel beds and banks requires a knowl-edge of the bottom velocity or flow velocity close to thebed. In a recent investigation of bank erosion areas alongthe Illinois River, Bhowmik and Schicht (1979) used thebottom velocity to determine bank stability.
The flow velocities measured at about 0.5 foot abovethe bed were plotted against the corresponding averagevelocity in the cross section. This plot indicated that theflow velocity at 0.5 foot above the bed can vary anywherefrom 70 to 95 percent of the average velocities in the cross
34
Figure 23. Comparison of average velocities for straight reaches
section. It is suggested that in stability analyses of beds orbanks, the critical velocity close to the bed correspondingto any discharge should be taken to be about 95 percentof the average velocity in the cross section. This shouldgive a conservative estimate of the bottom velocity in thestream.
Velocity Structure, lsovels
The point velocity data that were collected from boththe reaches for different discharges were made nondimen-sional by dividing these values with the correspondingaverage velocity in each cross section. The nondimensionalvelocities thus obtained were used to draw the isovels orlines of equal velocities at each cross section for all the dis-charges.
The isovels were plotted on coordinate paper followinga systematic procedure. The cross-sectional elevations wereplotted always keeping the right hand side of the river onthe right side of the graph. The right side of the graph paper
is based on the sense that an observer is assumed to belooking directly on the graph paper. The right side and theleft hand side of the river is based on the assumption thatone is looking downstream from a vantage point in the mid-dle of the river. Thus all the isovels illustrated will show theleft hand side of the river at or near the zero distance onthe horizontal scale. This type of uniformity is necessaryif any comparative study and/or analyses are to be donefrom the results obtained at different locations for varyingdegrees of discharge.
The discussion related to isovels is divided into two sub-sections, one for Reach 1 and the other for Reach 2.
Reach 1. Figures 25 through 29 show the isovels forReach 1 for an average discharge of 1040 cfs. This is thelowest discharge for which detailed velocity distributiondata were collected. The locations of all the cross sectionsare shown in figure 6. Note the gradual movement of thecore of the highest velocity from the center of the chan-nel in the straight reach toward the outside bank in thebend. A single core of high velocity flow is present at all the
3 5
Figure 24. Comparison of average velocities for bends
cross sections except 6 and 7 (figure 26) and possibly 13(figure 28). Note the approximate symmetrical distributionof the isovels in the straight reaches of the river at crosssections 16 and 17 (figure 29).
The distribution of the isovels and the shapes of thechannel are complex in cross sections 5 through 13 (figures26, 27, and 28). This is because of the presence of a num-ber of sharp bends of opposite direction at this location inthe river (figure 6). When the flow enters a bend, the highvelocity core moves toward the outside bank and staysclose to this bank for a considerable distance. However, ifa bend of opposite direction exists just downstream of thefirst bend, then the core of the high velocity flow locatednear the outside bank of the first bend will cross over thecenterline and move toward the outside bank of the down-stream bend near the end of the curved section of the river.
This is demonstrated in figure 26 for cross sections 5, 6,and 7 which are located in two consecutive bends of op-
posite curvature (figure 6).Because of the piling up of water near the outside bank
of the bends due to centrifugal force, sometimes a reversalof flow may occur near the inside bank of the bend. Cross
section 9 (figure 27) shows such a reversal of flow in thebend. Because of the presnece of a portion of eroded bankin the water just upstream of this cross section near the out-side bank, a reversal of flow also occurs near the outsidebank at this cross section.
The sectional elevation and the isovels at cross sections10, 11, and 12 (figures 27 and 28) clearly indicate thepresence of sand bars in the channel. The sand bar at crosssection 11 (figure 28) is in the middle of the stream and theflow is divided into two distinct zones on either side of thesand bar. Isovels at cross sections 12 and 13 (figure 28) and14 and 15 (figure 29) show the characteristic distributionof velocities in bends with higher velocities, steeper sideslopes, and deeper channel staying close to the outsidebanks. On the other hand, the symmetrical velocity struc-ture about the centerline, typical of the straight reaches, isquite evident at cross sections 16 and 17 (figures 29 and 6).
Figures 30 through 35 show the isovels for Reach 1 cor-responding to an average medium flow of 1420 cfs. Ve-locity distribution data were collected at only 15 cross sec-tions during this data collection trip.
36
Figure 25. lsovels for cross sections 1, 2, 3, and 4 in Reach 1 at low flow (average Q = 1040 cfs)
37
Figure 26. lsovels for cross sections 5, 6, and 7 in Reach 1 at low flow (average Q = 1040 cfs)
38
Figure 27. lsovels for cross sections 8, 9, and 10 in Reach 1 at low flow (average Q = 1040 cfs)
39
40
Figure 28, lsovels for cross sections 11, 12, and 13 in Reach 1 at low flow (average Q = 1040 cfs)
Figure 29. lsovels for cross sections 14, 15, 16, and 17 in Reach 1 at low flow (average Q = 1040 cfs)
41
Figure 30. lsovels for cross sections 1, 2, and 3 in Reach 1 at medium flow (average Q = 1420 cfs)
42
Figure 31. lsovels for cross sections 4 and 5 in Reach 1 at medium flow (average Q = 1420 cfs)
43
Figure 32. lsovels for cross sections 7 and 8 in Reach 1 at medium flow (average Q = 1420 cfs)
44
Figure 33. Isovels for cross sections 9 and 10 in Reach 1 at medium flow (average Q = 1420 cfs)
45
Figure 34. Isovels for cross sections 11, 12, and 13 in Reach 1 at medium flow (average Q = 1420 cfs)
46
Figure 35. lsovels for cross sections 14, 15, and 17 in Reach 1 at medium flow (average Q = 1420 cfs)
47
The characteristics of the isovels were almost identical tothose present during the low flow conditions. A single coreof high velocity flow was present in almost all cross sectionsexcept at sections 7 (figure 32), 10 (figure 33), and 11(figure 34). The locations of the cores of high velocity atsection 7 were identical for both the low flow and mediumflow conditions (figures 26 and 32). At section 11 (figure34) it appears that the sand bar present near the middle ofthe channel has started to divide the flow on two sides ofthe river in two distinct flow tubes. There was a large fallentree in the middle of the channel just a few hundred feetupstream of section 11. This tree acted as an obstacle to theflow, reduced the flow velocity in its leeward direction, andaccelerated the aggradation of the channel at this locationespecially during low flows. During low flows, the bulk ofthe water was flowing through the outside portion of thestream. However, during high flows, the whole width ofthe river was more or less effective in conveying the dis-charge. The isovels are symmetrical about the centerlinein the straight portion of the river, section 17 (figure 35).
Figures 36 through 39 show the isovels that were de-veloped for Reach 1 corresponding to a high average dis-charge of 4000 cfs. This discharge is about 4 times largerthan the low discharge of 1040 cfs, and more than 2.75times larger than the medium discharge of 1420 cfs. Inmany places, the low banks were flooded during this flow.In some instances, short circuiting of the flow on the flood-plain was observed, but the total amount of flow shortcircuiting was estimated to be very small. The floodplainsappeared to be acting as a storage reservoir rather than as aconveyance channel. Wherever the flooding of the low
lying floodplains was severe, the collection of velocity dis-tribution data was extremely difficult.
The isovels remained similar for low, medium, and highflows at cross sections 1, 2, and 3 (figures 25, 30, and 36).The cores of high velocity flows also stayed more or less atthe same relative position in the cross section. These ob-servations were also true for cross section 4 (figures 25, 31,and 37). In all these sections, with an increase in flow depthcorresponding to a higher discharge, the core of the highvelocity flows moved toward the water surface.
At cross section 5, the core of the high velocity flow wasvery close to the outside bank during the low and mediumflows (figures 26 and 31), but during the bankfull discharge,the core moved down and toward the inside bottom of thesection (figure 37). A general shift of the isovels towardthe inside bank of the section during this high flow is alsonoticeable. The effect of the bend near section 4 is to movethe high velocity flow toward the outside bank whichhappens to be the inside bank of the downstream bendclose to section 5. At bankfull discharges, the higher mo-mentum of the flow carried the high velocity core emergingfrom the bend near section 4 farther downstream keeping
it close to the inside bank near section 5 (figure 6) beforethe effect of the bend at section 5 could shift the coretoward the outside bank. This appears to be the mainreason why a shift in the core of the high velocity flows wasobserved between low, medium, and high flows. This alsoindicates that one cannot always expect to find the highvelocity flow near the outside bank of the bend for allpossible flow conditions. The flow frequency, the hy-draulic characteristics of the channel, and the antecedentconditions in the upstream channel determine the severityof the effects of any bend.
At cross section 6 (figure 37) only one core of highvelocity flow is present instead of the two cores that werepresent during low flow (figure 26). This core of high ve-locity flow is now closer to the bed and near the right handside of the bank. This is obviously the after-effects of theupstream bend near section 5 which has effectively movedthe high velocity flow toward the outside bank. The core ofhigh velocity flow remains close to the right bank down-stream.
Isovels at cross section 7 (figure 38) show the presenceof two cores of high velocity flows similar to those presentduring low and medium flows (figures 26 and 32). The corewith the higher velocity is now located close to the bed andnear the inside bank of the river. The position of this coreis a definite indication of the existence of a higher momen-tum of flow which has carried the high velocity core in arather short and straight route to section 7 from section 6.A considerable area of this cross section near the insidebank shows the presence of a large amount of reversedflow. The bend near section 7 is extremely sharp, resultingin a greater centrifugal force. High momentum associatedwith higher discharge and the sharpness of the bend havehelped to concentrate the flow near the outer two-thirdsof the channel. The combined effects of these factors is toforce a reversal of flow near the inside bank of the river(figure 6).
Isovels at cross section 8 (figure 38) show a single coreof high velocity flow near the left hand side of the river.Obviously it is an indication of the effect of the bendnear section 7 which has moved the high velocity flowtoward the outside bank of the river. This relative move-ment of the high velocity flow is similar to that observed atsection 6 (figure 37). With an increase in discharge, a signifi-cant amount of lateral movement of the high velocity flowtoward the left side of the river is also quite noticeable(figures 27, 32, and 38).
Isovels for cross section 10 are shown in figure 38. Notethe gradual movement of the core of the high velocity flowfrom near the centerline for low flow (figure 27), to theright side of the river for medium flow (figure 33), andfinally very close to the right side of the river for high flow(figure 38). This progressive lateral movement of the high
48
Figure 36. Isovels for cross sections 1, 2, and 3 in Reach 1 at high flow (average Q = 4000 cfs)
49
Figure 37. Isovels for cross sections 4, 5, and 6 in Reach 1 at high flow (average Q = 4000 cfs)
50
Figure 38. Isovels for cross sections 7, 8, and 10 in Reach 1 at high flow (average Q = 4000 cfs)
51
Figure 39. Isovels for cross section 11 in Reach 1 at high flow (average Q = 4000 cfs)
velocity flow at this cross section has resulted from a pro-portionate increase of the bend-effect near section 9 withan increase in discharge.
These and the other previous observations should makeit clear that the flow characteristics in a river will change inboth time and place as the discharge increases from low tohigher values. An increase in discharge not only increasesthe depth of water in a river, but it may also shift thepotential for bed and bank erosion. Velocity distributionsat cross sections 8 and 10 for various flow conditions showthat the bank which is stable and is not attacked by highvelocity flow during low and medium flows, may be subjectto the scouring action of high velocity flows during bank-full discharges as a result of its relative position in the river.
The bed of any river with a movable bed will shift underchanging flow conditions. Examination of the isovels atcross section 11 shows this quite clearly. Isovels at section11 are shown in figure 39. A comparison of the cross-sec-tional shapes at this location for low, medium, and highflows (figures 28, 34, and 39) indicate that the geometricalshape of the cross section has changed dramatically duringthe high flow. The hump or the sand bar that was presentnear the center of the channel during low and mediumflows is now completely absent. The bed material at this lo-cation is composed of sand (table 3). It appears that duringhigh flows, the river has worked over its bed, completelyscoured the sand bar and has developed a new shape at thislocation that is similar to a shape that can be expected in abend for a river with a movable bed. The differences in ele-vations between the highest point of the hump near thecenterline of the river and the lowest point on the bed near
the left bank are 5.8 feet for low flow (figure 28), 5.4 feetfor medium flow (figure 34), and only 1.8 feet for the highflow (figure 39). Section 10 which is just upstream of sec-tion 11 (figure 6) also showed a similar variation. The dif-ferences in elevation at section 10 between the hump andthe lowest point on the bed varied from 6.4 to 6.0 to 3 feetcorresponding to the low, medium, and high flows in theriver.
This observation related to the variability and changingshapes of the cross sections of natural rivers has consider-able practical implications. When a flood discharge is routedthrough a stream to determine the flood elevations, thecross-sectional shapes of the river are assumed to be thesame as those measured during low flows. In many cases,the river will scour its bed and banks, will change the shape
of the river, and may increase or decrease the cross-sectionalareas during flood flows. These changes will undoubtedlyhave an effect on the water surface elevations of the river.
Thus, the flood elevations, say for 100-year discharges, thatare presently determined by various agencies for floodplainmanagement may not always yield an accurate elevation
corresponding to the discharge in the river. Hydraulics offlow, transport of sediment, and the characteristics of thechanging bed forms in a sand bed channel must be consid-ered in any actual determination of flood elevations.
A comparison of the isovels developed for the three dif-ferent discharges has brought out some interesting phenom-ena. Generally, the average velocity in each cross section in-creased with an increase in discharge. But the numericalvalues of the ratio of the highest velocity to the average ve-
locity, taken from the plots of the isovels corresponding to
52
Table 7. Relative Magnitudes of the Maximum Nondimensional Velocities,Reach 1 (Figures 25 through 39)
Crosssection
Average Q=1040 cfs Average Q=1420 cfs
Maximum Maximum(fps) v/ (fps) v/
Average Q=4000 cfs,
Maximum(fps) v/
123456789
1 01 11 21 31 41 51 61 7
1.76 1.751.63 1.251.81 1.501.86 1.402.09 1.201.72 1.501.70 1.151.76 1.501.0 2.01.60 1.401.84 1.501.84 1.251.82 1.201.74 1.301.98 1.201.65 1.501.44 1.50
1.74 1.751.78 1.501.90 1.501.83 1.501.96 1.25
1.66 1.251.96 1.501.69 1.251.95 1.401.85 1.252.01 1.502.27 1.251.94 1.502.02 1.20
1.78 1.50
2.75 1.602.82 1.552.55 1.502.75 1.502.60 1.402.02 1.502.21 1.502.26 1.50
2.09 2.002.09 1.50
each cross section for various discharges, did not show anysignificant variation as the discharge increased from low tomedium to high flows.
Table 7 shows the average velocity and the ratio ofv/ for each cross section for the three discharges for whichdata have been collected. Except for cross section 10, theratio v/ at each section for three discharges remained prac-tically unchanged. This is quite remarkable consideringthat the discharge has increased four times from low tohigh flows. This constancy of the ratio v/ for differentdischarges at each section remained true for both thestraight reaches and bends. Thus, it appears that the maxi-mum velocity in a cross section can be estimated with rela-tive ease and confidence once the average velocity is eitherknown or computed from discharge and cross-sectionalareas. The average value of v/ for all the data shown intable 7 is 1.45. This means the average of the maximum ve-locities can be expected to be 145 percent of the averagevelocity in any cross section. The averages of all the averagevelocities at all cross sections for low, medium, and highflows were found to be 1.75, 1.89, and 2.41 fps, respec-tively.
Reach 2. Isovels similar to the ones shown in figures 25through 39 for Reach 1 have also been developed for Reach2. The procedure used was the same as that described forReach 1.
Figures 40 through 44 show the isovels at various cross
sections for Reach 2 corresponding to the low flow of 290cfs. This was one of the lowest flows for which velocity dis-
tribution data were collected. The frequency of occurrenceof this flow is 74 percent (table 6).
A single core of high velocity flow existed at all crosssections during this low flow condition. Quite evident evenduring such low flow conditions are the shifting of the highvelocity core from near the center at sections 1 and 2 to-ward the outside bank at sections 3 (figures 40 and 7) and 4(figure 41), the shifting back to the middle of the channelat section 5 (figure 41) where it starts to cross over towardthe other bank at section 6, and finally the crossing overand clinging to the outside bank of the bend at section 7(figure 42). Section 8 is more or less located at a crossingbetween two bends (figure 7) and the isovels at section 8(figure 42) show some symmetry in their distribution.
The cross-sectional shape at section 10 (figure 43) showsthe effect of the bend near section 9 (figure 7). The isovelsare not quite symmetrical at this location. Sections 11, 14,and 15 are located in the straight portion of the river, andsection 12 is located at the end of a long straight reach andnear the entrance of a bend. The isovels at sections 11, 14,and 15 (figures 43 and 44) show the symmetrical velocitydistribution typical of any straight reach of the river.
Figures 45 through 48 show the isovels for this reach forthe medium discharge of 2160 cfs. The frequency of occur-rence of this flow is about 40 percent (table 6). Thismedium discharge is about 7½ times the low flow of 290cfs for which velocity data were collected at this reach.
The isovels at sections 1 and 2 (figure 45) are identicalto those present during low flow (figure 40). Isovels at sec-
53
Figure 40. Isovels for cross sections 1, 2, and 3 in Reach 2 at low flow (average Q = 290 cfs)
54
Figure 41. Isovels for cross sections 4, 5, and 6 in Reach 2 at low flow (average Q = 290 cfs)
55
Figure 42. Isovels for cross sections 7 and 8 in Reach 2 at low flow (average Q = 290 cfs)
56
Figure 43. Isovels for cross sections 10, 11, and 14 in Reach 2 at low flow (average Q = 290 cfs)
57
Figure 44. Isovels for cross section 15 in Reach 2 at low flow (average Q = 290 cfs)
tions 3 and 4 (figures 45 and 46) show the characteristiclateral movement of the higher velocity as the flow passesaround the bend (figure 7). Isovels at section 5, which islocated at the crossing between two bends of oppositedirection, show the existence of a somewhat symmetricalvelocity distribution about the centerline. The core of thehigh velocity flow is quite close to the water surface, as itwas with low flow conditions (figure 41). At section 6(figure 46) the core of the high velocity flow is now closeto the inside bank of the bend (figure 7). This shifting ofthe high velocity flow has resulted from the higher mo-mentum of the flow associated with this relatively high dis-charge which is apparently trying to move the flow in theshortest distance possible, with a minimum amount ofmomentum transfer between various layers of flow. Thispattern of flow is the same as those observed at sections 6and 8 (figures 37 and 38) in Reach 1.
The isovels at section 7 (figure 47) show the presence oftwo cores of high velocity flow with one of the cores stay-ing close to the bed of the river. Section 8 is located at thecrossing between two bends of opposite direction in a seg-ment of the river with relatively straight alignment. Thestructure of the isovels is approximately symmetrical aboutthe centerline (figure 47). Section 11 is located quite a bitdownstream from the bend at section 9, but it still showsthe effect of this bend in its velocity structure. The high ve-locity core is biased toward the left hand side of the riverwhich in this case happens to be the continuation of theoutside bank of the bend at section 9.
Isovels at section 12 (figure 48) show that the core ofthe high velocity is close to the outside bank of the bend.The isovels at sections 14 and 15 (figure 48) are quite sym-metrical about the centerline. This indicates the establish-ment of a normal velocity distribution in the straight por-tion of the river at or near these sections.
Figures 49 through 53 show the isovels at Reach 2 forhigh flows with an average discharge of 3700 cfs. This flow
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is 13 times the low flows and about 1.75 times the mediumflow for which velocity distribution data were collected forthis reach.
Isovels at section 1 (figure 49) indicate that the highflow velocity is now shifted toward the right side of theriver. This is the effect of the bend at this location (figure 7)where the higher flow momentum is forcing the water totraverse a shorter path. Isovels at sections 2 and 3 (figure 49)are similar to those present during the low and mediumflows (figures 40 and 45).
The isovels shown in figure 50 for section 4 showthat the core of the high velocity flow has now definitelymoved toward the left side of the river which happens to bethe outside bank of the upstream bend (figure 7). Thisagain demonstrates the effect of the higher momentum as-sociated with higher discharges. Similar shifting of the highvelocity flow toward the outside bank is noticeable at sec-tion 5. Isovels at section 6 (figure 50) indicate that the coreof the high velocity flow is now in the deeper part of theriver and has moved close to the bend and near the outsidebank of the river. During low and medium flows, the highvelocity cores stayed close to the water surface.
At sections 7 and 8, the isovels have shifted toward theoutside bank (figures 51 and 7) and away from the watersurface moving downward near the bed. These rearrange-ments of the velocity structure resulted from the presenceof the upstream bend. Section 10, which is located down-stream of the bend near section 9, shows the eccentricity ofthe velocity structure with the higher flows staying relative-ly close to the left side of the river (figure 51).
Isovels at section 11 (figure 52) show the typical patternof velocity distribution in a straight segment of the river. Atsection 12, the isovels have shifted toward the inside bankof the river (figure 52). The velocity structures at sections14 and 15 (figures 53) are symmetrical about rhe centerlineof the river. These typical velocity distributions in thestraight portion of the river did not show much variability
Figure 45. Isovels for cross sections 1, 2, and 3 in Reach 2 at medium flow (average Q = 2160 cfs)
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Figure 46. Isovels for cross sections 4, 5, and 6 in Reach 2 at medium flow (average Q = 2160 cfs)
60
Figure 47. lsovels for cross sections 7, 8, and 11 in Reach 2 at medium flow (average Q = 2160 cfs)
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Figure 48. lsovels for cross sections 12, 14, and 15 in Reach 2 at medium flow (average Q = 2160 cfs)
62
Figure 49. lsovels for cross sections 1, 2, and 3 in Reach 2 at high flow (average Q = 3700 cfs)
63
Figure 50. lsovels for cross sections 4, 5, and 6 in Reach 2 at high flow (average Q = 3700 cfs)
64
Figure 51. Isovels for cross sections 7, 8, and 10 in Reach 2 at high flow (average Q = 3700 cfs)
65
Figure 52. Isovels for cross sections 11 and 12 in Reach 2 at high flow (average Q = 3700 cfs)
66
Figure 53. lsovels for cross sections 14 and 15 in Reach 2 at high flow (average Q = 3700 cfs)
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Table 8. Relative Magnitudes of the Maximum Nondimensional Velocities,Reach 2 (Figures 40 through 53)
Average Q=1040 cfs Average Q=1420 cfs Average Q=4000 cfs,
Cross Maximum Maximum Maximumsection (fps) v / (fps) v / (fps) v /
1 1.16 1.60 1.95 1.45 2.30 1.402 1.31 1.65 2.26 1.50 2.69 1.503 1.14 1.50 2.12 1.35 2.46 1.504 1.46 1.30 1.98 1.50 2.35 1.495 0.84 1.90 1.76 1.75 2.01 1.606 0.68 1.65 1.78 1.40 2.07 1.357 0.67 1.50 1.97 1.23 1.99 1.358 1.03 1.60 1.76 1.40 2.00 1.40
1 0 0.83 2.0 1.40 1.401 1 0.70 1.75 2.03 1.50 1.84 1.501 2 2.08 1.35 2.00 1.40
1 4 0.73 1.75 1.71 1.50 1.75 1.501 5 0.70 1.50 1.53 1.50 1.60 1.50
or change compared with the isovels that were developedfor the low and medium flows (figures 43, 44, and 48).
The velocity distribution data for Reach 2 for low,medium, and high flows showed quite a bit of similarity tothose analyzed for Reach 1. However, some dissimilaritieswere also observed for the two sets of data. Table 8 showsthe discharges, average velocities, and the ratio of the maxi-mum point velocity to the average velocity v/ in eachcross section corresponding to low, medium, and high flows.The ratio v/ is taken from the isovels shown in figures 40through 53. At all cross sections, the average velocityshowed a general increasing trend with an increasing dis-charge. The average of all the average velocities at all crosssections for various discharges is 0.94 fps for low flows,1.91 fps for medium flows, and 2.04 fps for high flows.This change is similar to that observed for Reach 1 (table 7).However, the maximum nondimensional point velocitiesv/ decreased somewhat as the discharge increased fromlow to medium to high flows. This is in constrast to the ob-servations made in connection with Reach 1 where themaximum average numerical values of v/ did not showmuch change from low to high flows. The reasons for thesevariations may be explained as follows.
Reach 2 is located about 75 miles downstream of Reach1. The river is wider at this location and the cross-sectionalareas of the river at bankfull discharges are much largerthan the cross-sectional areas at Reach 1 during bankfulldischarges. The ratios of the top widths to the averagedepths for bankfull discharges varied from about 9 to 16for Reach 1 and 11 to 16 for Reach 2. The average of thesevalues for Reach 1 is 12 and for Reach 2 is 13. The river inReach 2 is capable of carrying a higher volume of dischargecorresponding to any flow frequency compared with Reach1 (figure 18). The average invert slope for Reach 2 is about
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1.46 ft/mile compared to 0.95 ft/mile for Reach 1. Allthese factors have the combined effect of an even momen-tum transfer between various layers of flows at Reach 2 asthe discharge increases from low to higher values. This in-creased momentum transfer helps to redistribute the veloc-ity structure in both the horizontal and the vertical direc-tions. This is probably the reason why the differences be-tween the average velocity and the maximum velocity atReach 2 showed a progressive decrease as the dischargeincreased from low to medium to high flows.
Flow around Bends
Characteristics of the flow around bends have alreadybeen discussed under the heading “Velocity Distributions.”Some additional analyses of flow characteristics aroundbends are presented here.
Figures 54 and 55 show the distribution of the depth-averaged velocities in the verticals along the width of theriver at various cross sections for Reach 2. These data areshown for medium and high average discharges of 2160and 3700 cfs, respectively. The changes in the structureof the average velocities at different verticals are quite evi-dent in these two figures. Also shown is the shift of thehigh velocity flow toward the outside bank in the bends.
The lateral depth-integrated velocity distribution datawere also compared with the theoretical distribution sug-gested by Rozovskii (1957). The relationships used in thecomputation of the lateral velocity distribution are givenin figure 3. Typical plots for three cross sections are shownin figure 56. Here Vv is the depth-integrated velocity at anyvertical inside the bend and Vvm is the depth-integratedmaximum velocity at a vertical in the straight portion ofthe river. These data were collected during high flows in
Figure 54. Average velocity distribution in Reach 2 for medium flow
both reaches. Among the three cases shown, the correlationis good for two cross sections; however, for the third crosssection, the correlation is good except for the outside bankof the bend where predicted velocities are much lower thanthose measured.
Superelevations
The superelevations at bends in both reaches for differ-ent discharges were determined as the difference in watersurface elevations between the inside and the outside bankof the bends. Because of the extreme flatness of the riverprofile and low average velocities, the numerical values ofthe superelevations were rather small. In most instances, the
difference between the water surface elevations near theoutside and the inside banks of the bend was only a fewhundreths of a foot. However, there was an unmistakableinclination of the water surface at all bends especiallyfor medium and high flows.
In both reaches (figures 6 and 7) data related to velocitydistributions and water surface elevations were collectedfrom a minimum of one to a maximum of two to threecross sections in each bend. The superelevation measured atthe downstream section of the bend was assumed to be therepresentative superelevation in the bend.
Theoretical values of the superelevations were computedby use of equations 30, 31, 32, and 33. These equationsgave the theoretical values of the superelevations based on
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Figure 55. Average velocity distribution in Reach 2 for high flow
an assumed transverse velocity distribution in the bend fora constant velocity, free vortex pattern, forced vortex pat-tern, and a combination of forced vortex and free vortexpatterns, respectively. Superelevations were computed forthe medium and high flows in both reaches.
Figures 57a and b show the comparison between thecomputed and measured superelevations for Reach 1 andReach 2, respectively, for medium discharges only. In bothreaches, the superelevations computed by equation 32(forced vortex pattern) yielded consistently lower valuesthan those measured in the field. Superelevations computedby the other three equations showed quite a bit of vari-ability compared with the measured values. It appears thatfor practical purposes, either equation 30, 31, or 33 can be
70
utilized to estimate the superelevation in a natural river, be-cause none of the three equations was found to be superiorto the others.
The measured superelevations shown in figure 57 areclustered around some values which are multiples of a hun-dredth of a foot. This is because the water surface eleva-tions could not be measured closer than a hundredth of afoot.
The variability in the computed and measured values ofsuperelevations for the high discharges was similar to thatshown in figure 57. However, during high flows, the lowlying banks of the river were flooded and an accuratedetermination of the superelevation in the field was notalways possible.
Figure 56. Computed and measured lateral velocity distribution
Figure 57. Computed and measured superelevations
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Figure 58. Core of the high velocity flow for low, medium, and high flows in Reach 2
Secondary Circulation
Instrumentation and the necessary support were notavailable to collect data related to secondary currents in theriver during the present investigation. However, some gen-eralized comments can be made on the basis of the hydrau-lic and geometric data that were collected and analyzed forboth reaches.
The locations of the thalwegs for both reaches wereplotted on plan views to study the pattern of the shiftingthalwegs across the width of the channel. It was observedthat generally the thalwegs shifted toward the outside bankof the bend and continued to stay close to the outside bankfor some distance downstream until the downstream bendinitiated a shift in their positions. This shifting of thethalwegs results from the presence of the lateral componentof the velocity in and near the bends.
The isovels that were analyzed and presented previouslyalso showed some striking characteristics which demon-strated that the secondary currents not only exist in openchannels but also modify the velocity structure. Figure 58shows the positions of the cores of the high velocity flowsfor low, medium, and high flows in Reach 2. During lowflows, the high velocity flow followed the thalweg closelyin the upstream part, shifted toward the outside bank near
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section 7, and returned toward the centerline of the riverat section 8. Section 8 is located near the crossing betweenthe two bends.
For medium flow, the high velocity core remained closeto the centerline of the channel. However, for high flows,the core took a more direct route from section 1 to section2; stayed close to the left bank (outside bank) near sec-tions 3, 4, and 5; moved straight near the outside bankclose to section 6; and stayed at about the same locationfor the rest of the way to section 8. The variation of theshape of the high velocity core between low, medium, andhigh flows is associated with the changing characteristicsand magnitudes of the secondary currents in the same reachof the river.
The shapes of the isovels also tell us something aboutthe direction and presence of the secondary cells in an openchannel. Bathurst et al. (1977) measured currents in openchannel bends and found that the shapes of the isovelsare a good indicator of the direction and location of sec-ondary cells in the channel. If it is assumed that the isovelsare nothing but a set of flexible membranes held in place byfluids between them, then the bulging or the deformity intheir shape will indicate the presence of some force actingnormal to the face of the membrane. Thus, if the mem-branes bulge inward, it will indicate the presence of a force
Figure 59. Secondary current cells at low and high flows in Reach 2
from the outside to the inside and vice versa. If this tech-nique is followed through, the approximate locations of thesecondary cells can easily be identified and drawn in con-junction with the isovels. Such a plot is shown in figure 59for Reach 2. The data shown are for the low and high flowsat section 10. The shapes of the isovels indirectly give anexcellent clue as to the direction and the nature of the sec-ondary cells. As a matter of fact, any one of the isovelsshown in figures 25 through 53 could have been utilizedto develop plots such as those in figure 59.
An examination of figure 59 will show that the number,location, and nature of the secondary cells remained un-changed between low and high flows. Such similarity wasalso noted for other reaches of the river.
Equation 38 showed an empirical relationship for com-puting the magnitude of the angle of the secondary currentwith the longitudinal direction of flow on the outside bankof the river. The presence of this secondary current and thedeflection of the velocity vector was also substantiated byBrooks (1963). Brooks has mentioned that the maximum
73
74
Table 9. Energy and Momentum Coefficients
Cross Low flow Medium flow High Flowsection α β α β α β
Reach 11 1.62 1.22 1.95 1.38 1.47 1.142 1.39 1.14 1.83 1.38 1.39 1.133 1.33 1.12 1.60 1.25 1.43 1.144 1.25 1.09 1.57 1.24 1.44 1.155 1.22 1.09 1.13 1.01 1.13 1.026 1.62 1.22 1.45 1.177 1.13 1.05 1.48 1.21 1.33 1.088 1.45 1.16 1.67 1.26 1.34 1.109 2.54 1.66 1.38 1.16
10 1.31 1.11 1.49 1.22 1.74 1.2611 1.32 1.12 1.38 1.16 1.33 1.1112 1.32 1.12 1.54 1.2113 1.20 1.08 1.18 1.0614 1.26 1.10 1.56 1.2415 1.17 1.07 1.28 1.1116 1.45 1.1717 1.39 1.14 1.55 1.22
Reach 21 1.64 1.19 1.14 1.03 1.36 1.132 1.75 1.23 1.33 1.12 1.45 1.163 1.54 1.20 1.10 1.03 1.43 1.164 1.26 1.09 1.20 1.07 1.39 1.155 2.38 1.50 1.52 1.18 1.58 1.216 1.62 1.23 1.18 1.07 1.27 1.107 1.50 1.19 1.12 1.05 1.33 1.128 1.62 1.26 1.18 1.07 1.34 1.12
10 2.66 1.54 1.54 1.2311 1.87 1.30 1.20 1.07 1.44 1.1612 1.19 1.07 1.26 1.1014 2.06 1.38 1.23 1.09 1.51 1.2015 1.69 1.27 1.22 1.07 1.40 1.16
angularity of the secondary currents (ψ) observed by himin laboratory channels was 20 degrees. Equation 38 wasused to compute the angle ψ for high flow conditions atdifferent bends. It was observed that ψ varied from about9 to 66 degrees.
The higher values of ψ were associated with bendshaving shorter radius of curvature rc and larger centralangles ∆. With an increase in the value of ∆ and a decreasein the value of rc, the flow must turn around a sharper bendwith an associated greater change in the momentum flux ofthe flow. This change in the direction of the momentumflux and the larger centrifugal force will significantly in-crease the magnitude of the secondary currents.
Energy and Momentum CoefficientsThe energy coefficient α (equation 18) and the momen-
tum coefficient β (equation 19) were computed for eachsection for every discharge for which velocity data werecollected. The technique used was similar to that givenby Chow (1959).
Table 9 shows the numerical values of α and β for Reach1 corresponding to three different discharges. The averagevalues of α based on data from all the sections for low flowsis 1.41 and the corresponding average values of β is 1.16.Similarly, for medium flows, the average values of α and βare 1.51 and 1.21, respectively. The average values of α andβ during high discharges became 1.23 and 1.02, respectively.
The arithmetic means of all the α and β values for low,medium, and high flows are 1.41 and 1.14, respectively.
Table 9 also shows the α and β values for Reach 2 forthree discharges. The average values of α and β for lowflows are 1.80 and 1.28, for medium flows 1.22 and 1.08,and for high flows 1.41 and 1.26. The arithmetic means ofall the values of α and β for Reach 2 are 1.47 and 1.21, re-spectively.
The arithmetic means of all the values of α and β fromboth reaches are 1.44 and 1.17, respectively, The minimumand maximum values of α based on data from both reachesare 1.1 and 2.66, respectively. Similarly, the minimum andmaximum values of β based on data from both reaches are1.01 and 1.66, respectively.
The values of α and β shown in table 9 are from bothstraight reaches and bends. If these values for the straightreaches and bends are separated, the average values of α andβ are 1.45 and 1.22 for straight reaches and 1.43 and 1.18for bends. There is a slight decrease in these values in thebends compared with the straight reaches.
These average values appear to be within the limits thatwere reported by Hulsing et al. (1966) and Chow (1959).
Roughness Coefficient, Head Loss,and Energy Dissipation
Two of the most widely used roughness coefficients inopen channel flow analysis are Manning’s n and Chezy’s C,which can be computed by equations 15 and 13, respec-tively. Another form of roughness coefficient is expressedby C/(g)1 / 2 and is derived from Chezy’s equation. The in-terrelationships between C, n, and C/(g)1 / 2 are given byequations 16 and 17.
In the computation of n, C, and C/(g) 1 / 2 by equations15, 16, and 17, respectively, the values of average velocity ,average energy slope Se , and hydraulic radius R must beknown from field measurements. The values of and Rhave been determined for various discharges from the datameasured in the field. However, while computing the aver-age water surface slope and the average energy slope fromboth reaches for various discharges, it was observed that aconsiderable amount of additional head loss occurred inReach 2 for low, medium, and high flows at or near section13 (figures 7 and 20). This was caused by the presence ofbedrock at this location. The rock ledge acted as a low over-flow type dam in the course of the river especially duringlow flows and has consequently modified the water surfaceprofiles both upstream and downstream. The water surfaceprofile resembles an M1 type backwater curve downstreamof the rock ledge and an M2 type backwater curve upstreamof the rock ledge (Chow, 1959). An M1 curve is producedwhen the lower end of a long flume having a mild slope issubmerged in a reservoir to a greater depth than the normal
depth of flow in the flume. Whereas, an M2 type backwatercurve will result when the bottom of the flume at its lowerend is submerged in a reservoir to a depth less than thenormal depth.
This phenomenon is amply demonstrated in figure 60for three typical flow conditions. For the low flow condi-tion, the water surface profile starts to drop near section 12and continues to drop until near section 15. The approxi-mate drop of the water surface elevation at this location forthis flow is 1.2 feet. The average water surface slope up-stream of section 12 is 0.43 ft/mile and downstream ofsection 14 it is 1.25 ft/mile.
For medium flow, the control point has moved upstreamand is now located close to section 11 (figure 60). The aver-age drop of water surface at this location is 0.8 foot. Twodistinct water surface slopes exist for this flow condition.The average value of S w upstream of section 11 is 0.51ft/mile and downstream of section 14 it is 0.78 ft/mile.
In the case of high discharge, which was at or abovebankfull stages, the control point has moved upstreamnear section 9, a distance of about 4500 feet upstream fromsection 13. The average water surface drop at this locationis now close to 0.55 foot.
This change in the location of control points with an in-crease in discharge is the same as for flow over a low headsill in an open channel. The rock ledge, being immovableand nonerodible, acts as an obstacle in the path of the riverand consequently has changed the characteristics of flow.
The above discussion demonstrates that a single rough-ness coefficient for the entire length of Reach 2 should notbe computed. Either the additional head loss due to thepresence of the rock ledge must be subtracted from thetotal head drop before an average energy slope is computedor two separate slopes must be determined, one before thecontrol point and another after the control point. Thesetwo energy slopes can then be used in connection withequation 15 to compute Manning’s roughness coefficient n.This was done to compute the roughness coefficients forReach 2. However, for Reach 1, no such control pointexisted (figure 19) and a single line was fitted by the leastsquare technique to determine an average value of S w forall discharges.
Another necessary assumption in the computation of nwas that the average velocity at any section during asingle data collection trip did not vary significantly fromday to day. There was some change in the measured dis-charges from one day to the next in the same reach of theriver from section to section, but it is quite reasonable toassume that the average velocity at any section remainedapproximately unchanged during those consecutive daysof data collection when the discharge did not vary signifi-cantly. The water surface slope Sw and subsequently thevalue of Se needed to compute the values of n, C, and
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Figure 60. Water surface profile and head loss in Reach 2
C/(g) 1 / 2 was the value based on water surface elevationsmeasured during a single day.
Once the values of average velocity , energy coefficientα, and water surface elevation WS were known, the energyslope Se was computed by equation 42:
(42)
where WS1 and WS 2 are the water surface elevations atany two sections and L is the distance between these twosections. The other terms have already been explained.This procedure was used to compute Se either betweenany two sections or over the entire length of the studyreach.
The assumptions outlined above were necessary to com-pute a reasonable and representative value of the roughnesscoefficient on the basis of field data. At this point, it mustbe remembered that a natural channel does not behave likea laboratory channel where the discharge, water surfaceprofile, and other parameters can be kept constant over a
period of time. Therefore, in order to obtain any meaning-ful information from the data collected from a naturalchannel, simplification and a few generalized assumptionsmust be made before any computation can be done. It isthe contention of the author that the results obtained bythe above procedure should yield a representative value ofthe roughness coefficient in any natural channel.
Equations normally used in computing roughness coef-ficients in open channels are based on the assumption thatuniform flow exists in the river and that a unified roughnessparameter can be estimated. For the present case, uniformflow equations were used to estimate a composite roughnesscoefficient which should reflect the cumulative effects ofall resistance to flow in the river. This procedure does notshow the effect of the gain of potential energy for flowaround a bend, but it does show the effect of the normalresistance to flow in the channel. Following through withthese assumptions, the values of n, C, and C/(g)1 / 2 werecomputed for all flow conditions for both reaches.
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Table 10 shows the average values of Sw and Se, Man-ning’s n, Chezy’s C, and the values of C/(g) 1 / 2 for Reach 1corresponding to low, medium, and high flows. Computa-tions were made for each day for each set of data. The aver-age water surface slopes for low, medium, and high flowswere 1.57, 1.54, and 1.07 ft/mile, respectively. The averagevalues of Se varied from 1.58 ft/mile for low flow to 1.54ft/mile for medium flow to 1.15 ft/mile for high flow. Theaverage values of Sw and Se for corresponding dischargeswere almost identical, indicating an even energy dissipationover the whole length of this reach of the river.
The overall head loss h L in the river, computed by equa-tion 18 and expressed as a function of the unit length ofthe river, becomes equal to the numerical value of Se. ThusSe and hL are identical. Therefore, the values of Se shownin tables 10 and 11 also indicate the head loss in the riverfor different flow conditions.
The average values of Manning’s n for low, medium, andhigh flows are 0.051, 0.053, and 0.044, respectively. A de-crease in the value of n is associated with an increase in thedischarge. Chezy’s C varies from a minimum of 33 to amaximum of 55 for all flow conditions. The average valuesof C for low, medium, and high flows are 40, 40, and 51,respectively. Similarly, the average values of C/(g) l / 2 f o rthese flows are 7.1, 7.0, and 8.9, respectively.
Table 11 shows the values of Sw , Se, n, C, and C/(g)1/2
for the three flow conditions in Reach 2. For low andmedium flow conditions, computations were made bydividing the reach into two parts above and below the dis-continuity point of the water surface profile shown infigures 20 and 60. Computations were also made consider-ing the entire reach as a single unit with no discontinuity inthe water surface profile.
For low and medium flows between sections 1 and 8 or1 and 11, the values of Sw , Se, and n are smaller than thosebetween sections 1 through 15 or 14 through 15. Hereagain, the rock ledge near section 13 has effectively devel-oped a flatter water surface slope upstream of this sectionwhich in turn yields a smaller overall value of Manning’s nfor this reach of the river. For high flow conditions, it wasassumed that, on the average, a single water surface slopeexisted for the entire length of this reach and single valuesof n, C, and C/(g)1 / 2 were computed for the five days ofthe data collection (table 11). The average values of n, C,and C/(g) 1 / 2 for high flow are 0.043, 52, and 9.2, respec-tively.
The average overall values of n between sections 1 and15 for low, medium, and high flows are 0.041, 0.044, and0.043, respectively. The expected reduction in the values ofn with an increase in discharge did not really materialize atthis location because of the presence of a relatively flatwater surface slope during low flow upstream of section 13which resulted in smaller values of n during low flows. Datafrom both reaches indicated that the average overall values
of n can be as high as 0.053 and as low as 0.039.There was considerable variation in the hydraulic prop-
erties of the river between any two consecutive sections.Manning’s n was computed between successive sections forthree typical flow conditions corresponding to low, me-dium, and high flows for both reaches, as shown in figure61. In a few instances, there is discontinuity in the valuesof n because hydraulic data at these cross sections were notavailable on the specified date.
In Reach 1, the highest computed value of n is 0.084between sections 7 and 8 for medium flow and the lowestvalue of n is 0.028 between sections 14 and 15 for low flow.For Reach 2, the highest computed value of n is 0.073 be-tween sections 14 and 15 for low flow and the lowest valueis 0.013 between sections 5 and 8 for low flow. In general,the values of n in Reach 2 are lower upstream of section 11for all discharges (figure 61). This again demonstrates thesignificant effect of the rock ledge near section 13 on theoverall flow pattern in this segment of the river.
In the “Energy Dissipation” section of the backgroundanalysis it was mentioned that a plot of the ratio of Se /Swversus distance in an open channel can shed some light asto the nature of energy dissipation in the channel. Figure62 shows such a plot for Reach 1 for three typical flowconditions. The ratio Se /S w varies anywhere from 0.8 to1.4 indicating that in some part of the river, an acceleratingflow is present (Se/Sw >1) and in another part, the flow isdecelerating or a conversion of the kinetic energy into po-tential energy is taking place (Se/Sw < 1). This type ofvariability is expected in an open channel where the streambanks, bends, snags, and fallen trees change the patterns offlow. Consequently, the flow will pass through a series oflocalized acceleration and deceleration. However, in general,the flows in Reach 1 for all three flow conditions appear tohave been behaving much like a uniform flow pattern.
Figure 63 shows the variability of Se /Sw for Reach 2for three typical flow conditions. It appears that duringhigh flow conditions, the flow was accelerating consider-ably at or near section 4. Some deceleration of the flow isnoted near section 6. Otherwise Se/Sw varies close to unity.
If the ratio of the average energy slope S e (table 11) andthe bed slope S o (figure 60) between sections 1 through 11is computed, the value of Se/So becomes 0.14 for low flowdata collected on May 19, 1977. Similarly, for mediumflow, the ratio of Se/Sw for sections 1 through 11 is 0.18.For the high flow data shown in figure 60, the ratio S e /Sobetween sections 1 through 9 becomes 0.26. In all thesecases, the values of Se/So are much smaller than 1 indicatinga decelerating flow condition in this segment of the river.This again shows that a conversion of the kinetic energy in-to potential energy takes place in this reach of the riverwith an associated decrease in energy dissipation comparedwith uniform flow conditions. Thus, it is quite apparentthat the presence of bedrock, snags of permanent nature,
77
78
Table 10. Roughness Coefficient and Head Loss, Reach 1
Water surfaceslope, Sw
Energy slope,S e or bL Manning’s Cbezy’s
Date (ft/mi) (ft/mi) n C C/(g)1/2
Low flow10/20/75 1.29 1.29 0.043 46 8.210/21/75 1.96 1.98 0.061 33 5.810/22/75 1 54 1.56 0.054 37 6.610/23/65 1.57 1.57 0.043 46 8.110/24/75 1.48 1.50 0.053 38 6.7
Medium flow5/11/77 1.59 1.60 0.056 37 6.55/12/77 1.39 1.40 0.048 43 7.55/13/77 1.61 1.61 0.051 40 7.15/16/77 1.56 1.56 0.055 38 6.7
High flow3/20/78 1.18 1.26 0.046 48 8.53/21/78 0.90 0.96 0.040 55 9.73/22/78 1.09 1.16 0.044 50 8.83/23/78 1.12 1.20 0.045 49 8.6
Note. Sw, Se and bL were computed for the whole reach from cross section 1 to 17.
Table 11. Roughness Coefficient and Head Loss, Reach 2
Water surfaceslope, Sw
Energy slope,Se or bL Manning’s Cbezy’s
Date Cross section (ft/mi) (ft/mi) n C C/(g)1/2
Low flow5/17/77 1 to 8 0.43 0.44 0.022 79 13.95/18/77 1 to 11 0.36 0.38 0.028 63 11.2
14 to 15 1.27 1.28 0.074 25 4.41 to 15 0.96 0.96 0.040 43 7.6
5/19/77 1 to 11 0.39 0.40 0.029 62 10.914 to 15 1.25 1.26 0.073 25 4.4
1 to 15 0.97 0.97 0.041 43 7.6
Medium flow12/8/75 1 to 11 0.51 0.49 0.029 74 13.0
14 to 15 0.78 0.81 0.051 43 7.61 to 15 0.78 0.78 0.045 48 8.4
12/9/75 1 to 11 0.48 0.46 0.028 76 13.314 to 15 0.78 0.81 0.051 43 7.6
1 to 15 0.76 0.77 0.044 48 8.512/10/75 1 to 11 0.50 0.48 0.028 74 13.1
14 to 15 0.76 0.78 0.050 44 7.71 to 15 0.78 0.78 0.045 48 8.4
12/11/75 1 to 11 0.51 0.50 0.029 73 12.914 to 15 0.78 0.81 0.051 43 7.6
1 to 15 0.79 0.79 0.045 48 8.4
High flow12/05/77 1 to 15 0.68 0.70 0.045 50 8.812/13/77 1 to 15 0.68 0.70 0.045 50 8.812/14/77 1 to 15 0.71 0.73 0.046 49 8.612/15/77 1 to 15 0.53 0.55 0.040 56 9.912/16/77 1 to 15 0.49 0.51 0.039 58 10.1
Figure 61. Variation of Manning’s roughness coefficient
79
Figure 62. Ratio of Se/Sw for Reach 1
and other obstacles in the river course changes the charac-teristics of flow in the open channel.
The simple and basic analyses presented thus far are ex-tremely valuable in the study and subsequent understandingof the basic mechanics of flow in open channels.
Distribution of Unit Discharges
The detailed velocity distribution data collection for dif-ferent discharges for the present investigation required aconsiderable amount of time and was also very expensive.
80
However, if a correlation can be developed between thelateral velocities in each vertical with a parameter such asthe corresponding depths, then it will be very easy tomeasure the cross-sectional depths during low flows, andthen to estimate the lateral average velocities in each verti-cal for varying frequencies of discharges. In this study a re-lationship similar to equation 43 below was found to bevalid for both straight reaches and bends.
(43)
where q is the unit discharge at depth D, is the averageunit discharge in the cross section, is the average depth,K is a constant, and m is the coefficient of regression. A
Figure 63. Ratio of Se/S
w for Reach 2
8 1
Figure 64. Nondimensional unit discharge versus nondimensional depth
similar type of relationship was also postulated by Sium(1975).
Figure 64a shows a plot of versus for Reach 2for bankfull discharges where the data from the straightreaches and bends were plotted. Here K is 0.7 and m is 2.56.From other similar plots it was also observed that duringbankfull stages the spread of the points from a mean linewas less than that present during low flows. When the ratiosof and were close to or more than unity, the dif-ferences between the plotted points from straight reachesand bends were negligible. However, for smaller values of and , the difference became much more dominant,making the values of m usually greater than 2. Figure 64bshows other plots for bends relating and for bothreaches.
These two plots indicate that a correlation between and can be developed for open channel flows.This type of relationship is helpful in the determinationof an approximate lateral velocity distribution across thewidth of the channel once the individual depths are known.
82
Turbulence in an Open ChannelData related to the turbulent fluctuation of the velocity
component could not be collected because of the non-availability of support. Turbulent fluctuation of the ve-locity component is an important parameter and should beconsidered in the stability analysis of the bank in any openchannel flow problem.
Turbulent mixing is the main mechanism for diffusionand dispersion of momentum, heat, and mass in turbulentshear flows. It is also important in reaeration and sedimenttransport in streams. The measurement of turbulence instreams is very difficult because of the variation of tempera-ture of the water and the buildup of contamination on theturbulence measuring probes, such as a hot-film anemom-eter.
The best physical picture of turbulence is obtained byrecording the velocity fluctuations with time at variouspoints in the section of the stream. Kalinske (1942) ana-lyzed data collected from the Mississippi River which gavean indication of the turbulent velocity fluctuations. From a
statistical analysis of the Mississippi River data collected for10 minutes for each point, Kalinski concluded that theturbulent velocity fluctuations follow a Gaussian distribu-tion. Defining the standard deviation s or root-mean squareof the velocity fluctuations as the intensity of turbulence,Kalinski concluded that the maximum fluctuating compo-nent of the velocity (V'max - ) equal to 3s or greater oc-curs only for about 0.3 percent of the time. Thus, for allpractical purposes, the maximum value of (V´max – ) canbe taken as 3s.
The relative intensity of turbulence is defined by theratio of the standard deviation s to mean velocity i.e . , .From a plot of relative depth y/D versus the relative inten-sity of turbulence for both streams and pipes, Kalinske(1942) concluded that can easily be equal to l/3 nearthe boundaries. Thus with (V'max - = 3s and = l/3,the maximum point velocity can easily be 2 .
McQuivey (1973) collected longitudinal turbulence datafrom canals and rivers with a hot-film anemometer and or-dinary current meters. The current meter measurementswere made by changing the digital output from the currentmeter to an analog signal and recording the data on magnetictapes. These data were digitized for further analysis.
Comparison of longitudinal turbulence intensities mea-sured by McQuivey (1973) at the Mississippi River nearVicksburg, Mississippi, when the depth and width of theriver varied from 21 to 65 feet and 2000 to 2690 feet, re-spectively, showed that the longitudinal turbulence in-tensities measured by the current meter were always greaterthan those measured by the hot-film anemometer. The cur-rent meter measurements ranged from 0.066 at y/D of 0.88to 0.24 at y/D of 0.12 where the depth y is taken from thebed and D is the total depth of water at the point of mea-surement. The hot-film anemometer measurements variedfrom 0.043 at y/D of 0.88 to 0.15 at y/D of 0.12. In all themeasurements, the longitudinal turbulence intensity showedan increase with an increase in depth. The mean of the dif-ferences of the turbulence intensities measured by the cur-rent meter and by the hot-film anemometer was 0.053.
The hot-film anemometer measurements of the turbu-lence intensities at the Atrisco feeder canal and the RioGrande conveyance channel in Mexico were greater thanthose measured by the current meter (McQuivey, 1973).The Atrisco feeder canal was 1.4 to 1.9 feet deep and 56feet wide, whereas the Rio Grande conveyance channelwas 3.1 to 3.2 feet deep and 68 feet wide.
The discrepancy between this set of data and those col-lected from the Mississippi River may have resulted from adifference in the scale of the turbulence and the loss ofturbulence associated with the current meters due to inertialaveraging (Bennett and McQuivey, 1970). The roughnesselements and the depths are larger in deeper channels com-pared with those in shallower channels. Consequently, the
turbulence scale which is a function of the effective rough-ness element (Kalinske, 1942) must be larger in the deeperchannel compared with the shallow channel. Thus the lossof turbulence intensity due to “spectral averaging” by thepropeller will be less in the larger channels. This fact incombination with the higher velocities in the MississippiRiver may have contributed toward a smaller loss of turbu-lence intensity due to inertial averaging.
The above analysis indicates that the current meter cansometimes be used to measure the turbulence intensity inan open channel. However, if the direction of the currentmeter is not fixed, the freely rotating current meter willmeasure an average turbulence in the longitudinal direction.Depending upon the differences in water depths and flowvelocities, the turbulence intensity measured by the currentmeter may predict a higher or a lower value compared withthat measured by the hot-film anemometer.
The design and the analysis of open channel flow prob-lems should include a consideration for the turbulent ve-locity fluctuations of the flowing water. The analysis pre-sented so far showed a technique that can be used to esti-mate the magnitudes of turbulent velocity fluctuations. Thereason for including this analysis in the report is to empha-size the fact that turbulence is an important parameter inthe open channel flow problems.
Low Flow Characteristics: Pools and RifflesThe hydraulics of flow in a stream is usually different
for low flows than for bankfull or flood stages. During lowflows, the undulations in the bed and the roughness ele-ments of the bed will usually modify the local hydraulicsof flow, even though the overall gradient of the stream re-mains unchanged.
In a sand-gravel stream, pools and riffles will appearduring low flows. For some discharges, the flow may passthrough a critical stage (maximum discharge for this depth)at the riffle before returning to a placid condition in thepool. Whenever the bed materials are such that coarsegrained materials are present, the fine materials from theriffles are washed away and an armour where only thelarger particles remain is formed. The eroded fine grainedparticles are usually deposited in the pool.
Data from two pool-riffle sequences were collected dur-ing low flows from Reach 1 (figure 6). These data havebeen analyzed and some of the results were presented byBhowmik and Stall (1978a) at the 1978 Spring AnnualMeeting of the American Geophysical Union.
Figures 65 and 66 show the plan views of the two se-quences of pool and riffles where detailed hydraulic andgeometric data were collected. Out of the 51 bed materialsamples, 30 samples were collected from pool-riffle se-quence A (figure 65) with the remaining 21 samples col-
83
Figure 65. Plan view of pool-riffle sequence A
lected from pool-riffle sequence B (figure 66). The exactlocations of the bed and bank material samples are alsoshown. These bed and bank material samples were analyzedto determine the particle size distributions.
Tables 12 and 13 show the d50
and d 95 sizes, standarddeviation uniformity coefficient U, and some commentsas to the general nature of the materials based on the anal-ysis of the data from the two sequences. Normally, the bedmaterials at the riffle are coarser than those in the pools.The change in the sizes of the bed materials as the flowpasses from the riffle to the pool is shown in figure 67 asthe isolines of d
50 sizes in millimeters. The D50 sizes vary
from a maximum of 40 mm in the riffle for sample 6 (fig-ure 65 and table 12) to a minimum in the pool of 0.065mm for sample 19.
Isolines of d95 sizes for pool-riffle sequence A are alsoshown in figure 67. Here the d 95 sizes vary from a maxi-mum of 130 mm in the riffle, sample 2 (figure 65 and table12) to a minimum of 0.2 mm in the pool, sample 30. Thevariability and the areal distribution of the d95 sizes aresimilar to those observed for the d
50 sizes with the highest
sizes occurring in the riffles and the smallest sizes in thepools.
Figure 68 shows the lines of equal d50 and d 95 sizesfor pool-riffle sequence B. Here the largest size of themedium diameter is in the riffle with the lowest size oc-curring in the pool. The largest d 50 size of 4.6 mm is from
84
sample 41 (figure 66 and table 13) which is in the riffle,and the smallest value of d50 is 0.034 mm and is fromsample 32 in the pool section of the river. For sequenceB, the largest d95 size of 19 mm is in the riffle, samples36, 37, and 41 (figure 66 and table 13), and the smallestd 95 size of 0.2 mm is in the pool, sample 31. The generalpattern of the variability remained the same as that ob-served for the d50 sizes.
The hydraulic and geometric data that were analyzedfor the pool-riffle condition are the bed and water surfaceprofiles, velocity and velocity head, and the head loss. Fig-ure 69 shows the water surface and thalweg profiles forboth sequences of pools and riffles. There is a sharp drop inthe water surface elevation right after the riffle section. Thewater surface profile becomes extremely flat in the pool.
The head loss in pool-riffle sequence A was 4.44 ft/mileand for sequence B it was 2.48 ft/mile. The overall Manningsn was 0.034 in sequence A and 0.048 for sequence B.
Velocity distribution data were also used to determinevarious hydraulic parameters in the riffles. Figure 70 showsthe variability of velocity V, Froude number F, velocityhead V² /2g, and depth D in the riffle section of sequence A.The depth of water and the flow velocity changed in thetransverse direction. The Froude number is less than 1.0and has a maximum value of 0.7. The flow remained sub-critical throughout the riffle section. The water surfacewas wavey and a considerable amount of reaeration took
Figure 66. Plan view of pool-riffle sequence B
85
Table 12. Particle Size Characteristics of the Bed and Bank Materials,Reach 1, Pool-Riffle Sequence A
Samplenumber σ
123456789
101112131415161718192021222324252627282930
d 50 (mm) d (mm)95
36.0 71.024.0 130.021.0 70.014.0 57.0
0.19 0.3640.0 62.015.0 55.014.0 58.0
0.40 2.38.5 47.0
14.0 70.00.44 2.16.8 77.00.07 27.00.27 0.520.30 0.650.77 8.50.39 1.80.065 0.700.30 0.770.52 3.00.31 1.14.8 43.00.53 13.00.60 42.00.14 0.290.39 1.20.47 1.92.2 7.00.044 0.20
U Remarks
3.5113.764.87
11.582.531.858.83
16.911.89
21.44172.37
1.8412.1082.95
1.361.264.251.794.501.481.991.757.205.04
54.523.241.441.974.64
12.94
13.5587.5025.45
135.716.973.67
55.2695.24
2.05150.00262.50
2.0040.6329.17
1.751.362.851.76
13.911.782.111.94
18.977.68
1300.013.08
1.502.65
15.00
Gravelly sandGravelly sandDark brown gravelly sandDark brown gravelly sandBrown loamy sandBrown gravelly sandGravelly sandBrown gravelly sandBrown sandBrown gravelly sandBrown gravelly loamy sandBrown sandDark brown gravelly sandDark brown sandy loamBrown sandBrown sandBrown gravelly sandBrown sandSandy loamBrown sandBrown sandBrown sandGray brown gravelly sandDark brown gravelly sandBrown gravelly sandy loamLight brown loamy sandBrown sandBrown sandDark brown gravelly sandLight brown loam
place at the riffles. The general flow characteristics at allthe riffles in both test reaches did not show much variabilitywhen compared with each other.
The change in the bed material sizes and the variabilityin the Froude number from riffle to pool are shown in fig-ure 71 for sequence A. Higher values of d 50 , d 95 , and F areassociated with the riffles with correspondingly lower valuesin the pools. Similar variability was also observed in theother pool-riffle sequence.
Some correlations were observed between Froude num-ber F and the d
50 and d 95 sizes of the bed materials. Fig-
ure 72 shows such a relationship between F and the grainsizes. In general, higher values of Froude number are as-sociated with higher values of the bed material sizes.
Shield’s diagram (Simons and Sentürk, 1977) is normal-ly utilized in open channel flow analysis to determine thecritical shear stress on the bed of a stream. During lowflows, when the flow velocity approaches a critical valuenear the riffle, the bed materials may be exposed to a crit-
86
ical shear stress and it may initiate the bed scour. In orderto test whether or not the critical shear stresses on the bedapproached a value that can initiate the scouring of the bedmaterials, the nondimensional values of the shear stresswere plotted against the boundary Reynolds number infigure 73. In figure 73, d is the dimensionless shear stress,
o is the shear stress in pounds per square foot, γ s and γ arethe unit weights of bed particles and water respectively,d 50 is the median diameter of the bed materials, ℜ is theboundary Reynolds number, V* is the shear velocity in fps,and v is the kinematic viscosity of water in square feet persecond. All points except one plotted below the Shield’scritical curve indicating that the shear stresses in the pool-riffle sequence were below the critical shear stress for thetype and the sizes of bed material that are present in thisparticular reach.
During bankfull discharges, the effect of the pool andriffle on the overall flow condition is at a minimum. Forpool-riffle sequence A, the thalweg was near the right bank
87
Table 13. Particle Size Characteristics of the Bed and Bank Materials,Reach 1, Pool-Riffle Sequence B
Samplenumber d50(mm) d95(mm) σ U Remarks
31 0.030 0.20 Brown silt loam32 0.034 0.24 6.34 Brown silt loam33 0.39 1.2 1.79 1.73 Sand34 0.17 0.36 1.39 1.64 Light brown sand35 1.2 13.0 10.03 43.14 Dark brown gravelly
loamy sand36 4.0 19.0 6.50 20.00 Brown gravelly sand37 3.4 19.0 5.09 14.85 Dark brown gravelly sand38 2.4 18.0 5.85 17.62 Brown gravelly sand39 0.027 0.21 3.94 19.55 Silt loam40 0.21 0.48 1.38 1.53 Brown sand41 4.6 19.0 3.86 12.77 Dark brown gravelly sand42 0.65 6.5 2.57 2.75 Brown gravelly sand43 0.80 14.0 6.60 13.68 Gravelly sand44 0.12 0.25 2.33 6.84 Brown sandy loam45 0.28 1.0 1.84 2.50 Light brown sand46 0.50 1.6 1.79 2.39 Brown sand47 0.10 7.0 17.58 42.86 Dark brown sandy loam48 0.12 0.33 3.36 12.50 Light brown sandy loam49 0.17 0.36 1.24 1.31 Light brown sand50 0.30 0.59 1.40 1.82 Brown sand51 0.054 0.46 7.05 Dark gray brown loam
Figure 67. Isolines of d50 and d95 sizes of bed materials for pool-riffle sequence A
Figure 68. lsolines of d50 and d95 sizes of bed materials
for pool-riffle sequence B
Figure 69. Thalweg and water surface profiles for pool-riffle sequences A and B
88
Figure 70. Hydraulic and geometric characteristicsin the riffle section of sequence A
Figure 71. Distribution of bed material sizes and Froude number in pool-riffle sequence A 89
Figure 72. Average Froude number versus grain size in pool-riffle sequence A
Figure 73. Shield’s diagram for pool-riffle sequence A
for low flows, but for bankfull discharges the thalweg re-mained close to the left bank. However, the ratio of thelengths of the thalwegs for the entire reach for low and highflows was computed to be about 1. Because of the restraintexerted by the banks, the location of the thalweg duringhigh flows was different from that during low flows, butthe total length of the thalweg for both low and high flowsremained about the same.
Data analyzed here indicate that when the river flowsthrough a series of pools and riffles, the water surface pro-
90
file and the invert slope are rather steep in the riffle andmilder in the pools, the average velocity and Froude num-ber change from high to low from riffle to pool, the bedmaterial sizes change from coarser to finer in the riffle-poolsequence, and considerable reaeration takes place in the rif-fles. These low flow characteristics are rather ideal formaintaining a balanced aquatic life in the stream environ-ment because they provide adequate water depths and foodsupply in the pools and possibly sufficient dissolved oxygento the water near the riffles.
SUMMARY AND CONCLUSIONS
The hydraulics of flow was investigated at two reaches inthe Kaskaskia River. One of the reaches is located about 12miles downstream of Lake Shelbyville and the other reachis located about 7 miles downstream of Carlyle Lake.
Hydraulic data were collected for flows of 58, 1040,1420, and 4000 cfs from the reach below Lake Shelbyvilleand for flows of 290, 2160, and 3700 cfs from the reachbelow Carlyle Lake. The flow frequencies varied from 5 to88 percent. A total of 79 bed and bank material sampleswere collected and analyzed to determine the particle sizedistribution of these materials.
Geomorphologically the Kaskaskia River has passed theyoung stages of development and is presently in an equilib-rium or mature stage of development. The bed materials inboth reaches are sandy in nature and the average mediandiameter of the bed materials is about 0.39 mm. The cross-sectional shapes of the river in the straight reaches are gen-erally trapezoidal, whereas in the bends, the cross-sectionalshape is skewed with the maximum depths occurring nearthe outside bank of the bend where they are about 30 to 90percent more than the average depths in the river.
Analyses of the water surface profiles and the energygrade lines indicate that, in most cases, the flow can be ap-proximated by uniform flow equations. However, in Reach2, the presence of a rock ledge contributed toward addi-tional head loss. Head loss varied from 0.96 ft/mile for highflows to 1.98 ft/mile for low flows in Reach 1. Similar vari-ability was also observed in Reach 2.
The vertical velocity distribution was found to follow alogarithmic distribution. The average depth-integrated ve-locities were 5 to 7 percent smaller than the average ve-locity determined from two point measurements in eachvertical. The average velocity at 0.5 foot above the bed wasapproximately 95 percent of the average velocity in thecross section.
A total of 79 isovels or lines of equal velocities in thecross sections were developed from the hydraulic data col-lected in the field. The lateral velocity distribution in thestraight portion of the river was found to be symmetricalabout the centerline. However, in the bends, the velocitydistribution was skewed with the high velocity cores stayingclose to the outside banks of the bends. Higher momentumof flow associated with increased discharge sometimesforced the cores of high velocity flow to move in a ratherdirect route in the stream and have thus changed the vulner-able location of the bank and bed for erosion and scour.Shifting of the high velocity cores was observed with chang-ing discharges.
The average velocity increased as the discharge increasedin the river. But the ratio of the maximum velocity to theaverage velocity remained almost unchanged for low, medi-um, and high flows. The maximum average velocity was
about 145 percent more than the average velocity. In a fewsections, considerable amounts of bed scour took place dur-ing high flows.
A theoretical distribution was found to predict the lateralvelocity distribution in the bend satisfactorily. The magni-tude of the superelevation in the bend was small. At least 3theoretical equations predicted the superelevation withinthe same percent of accuracy. Direction, pattern, and thenumber of secondary circulation cells in the bends and alsoin the straight reaches can be sketched on the basis of theisovels developed for the cross sections. The number ofcells was found to be the same for low, medium, and highflows.
The average value of the energy coefficient was 1.45 forstraight reaches and 1.43 for bends. Similarly the averagevalue of the momentum coefficient was 1.22 for straightreaches and 1.18 for bends. Better momentum exchangein the bends helped to reduce the numerical values of theenergy and momentum coefficients in the bends.
Average Manning’s roughness coefficients varied from aminimum of 0.039 to a maximum of 0.053. Roughnesscoefficients showed a decrease in value with an increasein discharge. In Reach 2, the presence of a bedrock ledgehas changed the flow characteristics making the low andmedium flow conditions similar to the flow over a low over-flow type structure.
It was shown that the ratio of the energy slope Se to thewater slope Sw or to the bed slope So is a good indicatorof the energy dissipation characteristics of the river. ForSe/So> 1, the flow is accelerating and for Se/So< 1, theflow is decelerating and backwater effects are indicated.
Analyses of the unit discharges across the width of theriver have shown that the unit discharges for various flowconditions are proportional to the respective water depthsin the section. Thus a knowledge of the water depths canbe utilized to estimate the distribution of the dischargesacross the width of the channel.
Turbulence in an open channel flow is very importanttoward determining the stability of bed and banks andits magnitude can sometimes be measured with the helpof an ordinary current meter.
The low flow characteristics of a river are different fromthose present during medium and bankfull stages. The riverflows through a series of pools and riffles with larger diam-eter bed material in the riffle and fine materials in the pool.The median diameter varied from 40 mm in the riffle to0.04 mm in the pool. The Froude number varied from 0.7in the riffle to 0.01 in the pool. Head loss was about 2.48ft/mile in one pool-riffle sequence and about 4.44 ft/milein the other. During high flows, the pool and riffles are allsubmerged and their effects on the overall flow conditionare minimal or nonexistent.
91
REFERENCES
American Society of Civil Engineers. 1963. Friction factorsin open channels. Proceedings ASCE, Journal of the Hy-draulics Division v. 89(HY2):97-143.
Barnes, H. H., Jr. 1967. Roughness characteristics of naturalchannels. U.S. Geological Survey, Water-Supply Paper1849, U.S. Government Printing Office, Washington,D.C.
Bathurst, J. C., C. R. Thorne, and R. D. Hey. 1977. Directmeasurements of secondary currents in river bends. Na-ture, v. 269(5628):504-506.
Bennett, J. P., and R. S. McQuivey. 1970. Comparison of apropeller flowmeter with a hot-film anemometer in mea-suring turbulence in movable-boundary open-channelflows. U.S. Geological Survey, Professional Paper 700-B:B254-B262.
Bhowmik, N. G. 1968. The mechanics of flow and stabilityof alluvial channels formed in coarse materials. Ph.D. dis-sertation, Colorado State University, Fort Collins, 207 p.
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93
=
============
=
==
========================
=
======
A
A1a
B1bC
CfcD
g
ℜ
oS
D max
d
d fd
15.9,d
35
d50, d 60
d84,
d84.1d 85, d 95
FF iff sf ss
hLI ri
jKk, k
1
k slLM 1
, M2
Mmm
lnPQq,
Rr, rc ,r ,ri
cSeSoSPS RSws
NOTATIONS
Cross-sectional area in square feetConstant, nondimensionalCoefficientConstant, nondimensionalCoefficientChezy’s coefficient in one-half power of feet per secondCentrifugal forceCoefficientTotal depth of water at any vertical in feetMaximum depth in feetAverage depth in feetDepth of water at any point in the cross section in feetFall diameter of the bed material in feet
Size of the bed materials where 15.9, 35, etc. percent ofthe particles are finer than these respective sizes in mm or feet
Froude number, nondimensionalBody force in the ith directionDarcy-Weisbach friction factor, nondimensionalSilt factorSeepage force in pounds per square footAcceleration due to gravity in feet per second squaredHead loss in feetTransverse inclination of the water surface, nondimensionalCoefficientCoefficientCoefficientCoefficientsEquivalent roughness length in feetCoefficientLength between any two cross sections in feetTypes of backwater curves on mild slopeMomentum in poundsCoefficient of regressionCoefficientManning’s roughness coefficientPressure force in poundsDischarge in cubic feet per secondUnit discharge and average unit discharge, respectively, in cfs per footReynolds numberHydraulic radius in feetRadius of curvature, radius of centerline, inside radius of curvature,and outside radius of curvature of bends, respectively, in feetShape factor of the cross section, nondimensionalSlope of energy gradelineSlope of the bedShape factor of the particles, nondimensionalShape factor of the reach, nondimensionalWater surface slopeStandard deviation of the turbulent velocity fluctuation
94
NOTATIONS (Concluded)
tUui
u 'iu ´ u´i jV
VV
max
vVvm
V *V'V'maxvWWPWSwXX'x ixjYY´yZαβγγs∂
∆ P∆∆ Z
∆ '
kµνρfσ
od
φψ
ω
===
=
=
=====
==================================
=
Time in secondsUniformity coefficient, d60 / d 10 ,nondimensionalMean velocity in the ith direction in feet per second
Turbulent velocity component in the ith direction in feet per second
Reynolds stress
Velocity in feet per secondAverage velocity in feet per secondMaximum average velocity of any vertical in feet per secondAverage velocity in any vertical in a section in feet per secondMaximum average velocity at a vertical in the straight portionof the stream in feet per secondShear velocity in feet per secondVv/Vvm, nondimensionalMaximum turbulent component of the velocity in feet per secondPoint velocity in feet per secondTop width of the cross-section in feetWetted perimeter in feetWater surface elevation in feet above mean sea levelDistance of a vertical from the bankDistance in the downstream direction in feetDistance of any vertical from the centerline in feetDistance in the ith direction in feetDistance in the jth direction in feetDistance normal to the bed in feetDistance in a vertical direction in feetDistance of any water layer from the bed in feetDistance in the transverse direction in feetEnergy coefficient or Coriolis constant, nondimensionalMomentum coefficient, nondimensionalUnit weight of water in pounds per cubic footUnit weight of particles in pounds per cubic footPartial derivative, nondimensionalPressure force
Dynamic viscosity of water in pound-second per square footKinematic viscosity of water in square feet per secondDensity of fluidStandard deviation of the bed or bank materials, nondimensionalShear stress in pounds per square footDimensionless shear stressBed inclination, nondimensionalAngle of the velocity vector on the outside bank in a bend withthe normal flow direction in degreesFall velocity of the bed materials in feet per second
Deflection angle of the bend in degreesSuperelevation in feet
Universal constant equal to 0.4
95
96
APPENDIX A. VELOCITY DISTRIBUTION DATA, KASKASKIA RIVER BELOW LAKE SHELBYVlLLE
Cross Section Number 1 Cross Section Number 3 Date of data collection 10/20/75 Date of data collection 10/21/75 Measured discharge 1106 cfs Measured discharge 1125 cfs Cross-sectional area 629 sq ft Cross-sectional area 623 sq ft Average velocity 1.76 fps Average velocity 1.81 fps Water surface elevation above msl Water surface elevation above msl
Left bank 512.50 ft Left bank 512.17 ft Right bank 512.49 ft Right bank 512.17 ft
Distance along the centerline between cross sections 0
Distance along the centerline between cross-sections 2 to 3 400 ft
Distance from the right side looking
Average velocity in the vertical
Distance from the right side looking
Average velocity in the vertical
downstream (ft) Depth of water (ft) (fps) downstream (ft)
Depth of water (ft) (fps)
24 REW 11 REW 30 5.4 0.66 15 2.8 0.79 35 6.9 1.37 20 6.0 0.96 40 7.3 1.37 25 7.3 1.00 50 7.0 1.54 30 6.9 1.30 55 6.8 1.65 35 6.7 1.55 60 7.0 2.15 40 6.8 1.84 70 6.6 2.53 50 6.5 2.12 75 6.7 2.62 60 6.0 2.23 80 7.1 2.47 70 6.1 2.30 85 6.4 2.38 80 6.4 2.12 90 7.4 2.37 90 6.5 2.09 95 7.0 2.07 95 6.4 2.16
100 8.1 1.93 100 6.4 1.87 105 8.7 1.78 105 6.3 1.57 110 7.5 0.55 110 4.8 1.18 115 4.8 0.37 115 2.3 0.73 117 4.5 0.39 120 LEW 121 LEW
Cross Section Number 4 Cross Section Number 2 Date of data collection 10/21/75 Date of data collection 10/20/75 Measured discharge 1159 cfs Measured discharge 1058 cfs Cross-sectional area 622 sq ft Cross-sectional area 649 sq ft Average velocity 1.86 fps Average velocity 1.63 fps Water surface elevation above msl Water surface elevation above msl Left bank 512.12 ft
Left Bank 512.23 ft Right bank 512.12 ft Right bank 512.21 ft
Distance along the centerline
between cross sections 3 to 4 363 ft Distance along the centerline between cross sections 1 to 2 1300 ft
Distance from the Average velocity right side looking
Depth of in the vertical Distance from the
right side looking Average velocity
in the vertical downstream (ft) water (ft) (fps) downstream (ft)
Depth of water (ft) (fps) 4 REW
6 REW 10 3.1 0.36 10 6.2 0.57 15 4.0 0.81 15 6.7 0.83 20 4.9 1.55 20 6.5 1.04 25 5.2 1.66 25 6.7 1.24 30 5.2 1.77 35 6.3 1.61 40 5.8 2.02 45 6.3 1.96 50 6.1 2.02 55 6.3 2.00 60 8.1 1.91 65 6.0 2.01 70 8.8 2.02 75 5.8 2.17 75 9.0 2.10 85 5.6 2.02 80 9.1 2.05 90 5.6 1.96 85 9.6 1.99 95 5.5 1.62 90 10.0 1.75
100 5.2 1.74 95 8.2 1.44 105 5.2 1.71 100 6.5 0.73 110 5.0 1.31 105 4.3 0.33 115 3.9 0.95 112 LEW 117 3.2 0.75 120 LEW
Note. REW = Right edge of water looking downstream LEW = Left edge of water looking downstream
97
APPENDIX A. Continued — Shelbyville
Cross Section Number 5 Cross Section Number 7Date of data collection 10/21/75 Date of data collection 10/22/75Measured discharge 1177 cfs Measured discharge 1030 cfsCross-sectional area 560 sq ft Cross-sectional area 605 sq ftAverage velocity 2.09 fps Average velocity 1.70 fpsWater surface elevation above msl Water surface elevation above msl
Left bank 511.89 ft Left bank 510.95 ftRight bank 511.95 ft Right bank 510.86 ft
Distance along the centerlinebetween cross sections 4 to 5 1016 ft
Distance along the centerlinebetween cross-sections 6 to 7 748 ft
Distance from theright side looking
Average velocityin the vertical
Distance from theright side looking
Average velocityin the vertical
downstream (ft)Depth ofwater (ft) (fps) downstream (ft)
Depth ofwater (ft) (fps)
14 REW 10 REW16 6.5 2.28 14 1.0 1.0220 8.0 2.38 18 2.2 1.2224 9.5 2.50 25 4.7 1.4930 11.0 2.37 30 5.8 1.4935 11.3 2.37 35 6.3 1.7340 10.9 2.32 45 7.0 1.7745 10.4 2.24 55 8.2 1.8350 8.9 2.12 65 11.0 1.6360 6.2 2.14 70 12.1 1.6070 4.4 1.81 75 12.1 1.6780 2.4 1.84 80 11.5 1.6685 2.7 1.57 85 9.4 1.7890 2.9 1.03 90 6.9 1.8295 2.5 0.33 93 3.8 1.46
100 1.8 0.0 95 LEW105 LEW
Cross Section Number 6 Cross Section Number 8Date of data collection 10/21/75 Date of data collection 10/22/75Measured discharge 1170 cfs Measured discharge 989 cfsCross-sectional area 680 sq ft Cross-sectional area 563 sq ftAverage velocity 1.72 fps Average velocity 1.76 fpsWater surface elevation above msl Water surface elevation above msl
Left Bank 511.81 ft Left bank 510.72 ftRight bank 511.78 ft Right bank 510.71 ft
Distance along the centerlinebetween cross sections 5 to 6 448 ft
Distance along the centerlinebetween cross sections 7 to 8 452 ft
Distance from theright side looking
Average velocityin the vertical
Distance from theright side looking
Average velocityin the vertical
downstream (ft)Depth ofwater (ft) (fps) downstream (ft)
Depth ofwater (ft) (fps)
12 REW18 5.4 0.22 4 REW24 6.7 0.96 12 5.7 0.8230 6.0 .93 20 7.7 1.2735 5.9 1.15 25 8.0 1.8942 6.0 1.54 30 7.8 2.0450 5.5 1.88 40 7.8 2.4260 5.7 2.63 50 7.5 2.3070 6.3 2.28 60 6.5 1.9880 6.5 2.24 70 5.9 1.7790 6.7 2.33 75 5.3 1.50
100 6.5 2.04 80 5.1 1.48105 6.5 1.93 85 3.7 1.19110 6.7 1.85 90 2.7 1.33115 6.4 1.54 95 2.2 1.05120 5.7 0.84 100 1.6 0.86125 2.3 -0.36 103 1.4 1.19127 1.4 -0.34 106 LEW132 LEW
98
APPENDIX A. Continued — Shelbyville
Cross Section Number 9 Cross Section Number 11 Date of data collection 10/22/75 Date of data collection 10/22/75 Measured discharge 1171 cfs Measured discharge 953 cfs Cross-sectional area 1173 sq ft Cross-sectional area 518 sq ft Average velocity 1.00 fps Average velocity 1.84 fps Water surface elevation above msl Water surface elevation above msl
Left bank 510.64 ft Left bank 510.28 ft Right bank 510.64 ft Right bank 510.13 ft
Distance along the centerline between cross sections 8 & 9 552 ft
Distance along the centerline between cross sections 10 & 11 620 ft
Distance from the right side looking downstream (ft)
Depth of Water (ft)
Average velocity in the vertical
(fps)
Distance from the right side looking downstream (ft)
Depth of Water(ft)
Average velocity in the vertical
(fps)
9 REW 16 REW 17 3.8 -1.31 20 3.4 1.37 22 7.0 0.66 25 5.3 1.99 27 8.0 0.69 30 5.6 1.97 32 10.6 0.94 35 6.2 2.01 37 11.9 1.25 40 6.3 1.94 47 12.7 1.43 50 4.7 1.91 57 12.7 1.76 60 3.3 1.95 67 13.3 1.58 70 2.4 2.04 77 12.8 1.25 80 2.8 1.96 87 12.2 1.17 90 2.7 2.37 97 8.5 0.91 100 3.5 2.34
107 6.5 0.96 105 5.4 1.90 112 6.9 -0.14 110 7.1 0.81 117 6.3 -0.30 115 8.2 1.77 122 6.1 -0.27 120 8.1 1.86 127 5.4 -0.23 125 6.7 1.49 132 8.5 -0.14 130 3.5 0.92 136 LEW 134 LEW
Cross Section Number 10 Cross Section Number 12 Date of data collection 10/22/75 Date of data collection 10/23/75 Measured discharge 940 Measured discharge 984 cfs Cross-sectional area 586.0sq ft Cross-sectional area 534 sq ft Average velocity 1.60 fps Average velocity 1084 fps Water surface elevation above msl Water surface elevation above msl
Left bank 510.50 fr Left bank 509.72 ft Right bank 510.51 ft Right bank 509.70 ft
Distance along the centerline between cross sections 9 to 10 420 ft
Distance along the centerline between cross sections 11 & 12 972 ft
Distance from the right side looking downstream (ft)
Depth of Water(ft)
Average velocity in the vertical
(fps)
Distance from the right side looking downstream (ft)
Depth of Water(ft)
Average velocity in the vertical
(fps)
16 REW 33 REW 20 5.9 1.00 37 2.2 1.00 25 8.3 1.35 42 2.9 1.19 30 8.9 1.23 47 3.5 1.06 35 8.6 0.92 52 4.3 1.21 40 8.4 1.56 58 5.5 1.52 50 7.0 1.66 65 5.9 1.86 60 5.5 1.95 75 5.6 1.83 70 4.1 2.01 85 5.6 2.05 80 3.2 2.02 95 5.8 2.47 90 3.3 1.94 105 6.4 2.04
100 3.9 1.91 110 6.7 2.16 110 4.0 1.89 115 7.0 2.11 115 4.0 1.91 120 7.2 1.99 120 3.9 1.65 125 6.5 1.62 125 3.3 1.43 130 5.1 1.39 130 2.3 1.22 132 4.5 1.22 135 LEW 136 LEW
APPENDIX A. Continued — Shelbyville
Cross Section Number 13 Cross Section Number 15Date of data collection 10/23/75 Date of data collection 10/23/75Measured discharge 933 cfs Measured discharge 954 cfsCross-sectional area 512 sq ft Cross-sectional area 481 sq ftAverage velocity 1.82 fps Average velocity 1.98 fpsWater surface elevation above msl Water surface elevation above msl
Left bank 509.57 ft Left bank 509.45 ftRight bank 509.65 ft Right bank 509.44 ft
Distance along the centerlinebetween cross sections 12 & 13 320 ft
Distance along the centerlinebetween cross sections 14 & 15 552 ft
Distance from theright side lookingdownstream (ft)
Depth ofWater (ft)
Average velocityin the vertical
(fps)
Distance from theright side lookingdownstream (ft)
Depth ofWater (ft)
Average velocityin the vertical
(fps)
12 REW 14 REW15 6.5 1.53 17 1.0 018 8.9 1.33 20 1.8 0.6622 10.2 1.81 25 2.2 1.1927 11.9 2.01 30 2.9 1.4632 12.0 2.02 35 3.7 1.6137 10.0 2.01 40 4.0 1.7542 8.9 1.88 45 4.6 1.7150 6.8 1.84 55 5.5 2.0660 4.5 1.64 65 6.9 2.0870 4.0 1.82 75 7.6 2.1775 3.5 1.71 80 7.8 2.1480 2.5 1.60 85 9.0 2.1285 2.4 1.49 90 10.0 2.1790 1.5 1.23 95 7.8 2.0495 0.7 0.77 100 3.7 2.15
100 LEW 105 1.7 1.37108 LEW
Cross Section Number 14 Cross Section Number 16Date of data collection 10/23/75 Date of data collection 10/24/75Measured discharge 945 cfs Measured discharge 950 cfsCross-sectional area 544.0sq ft Cross-sectional area 575 sq ftAverage velocity 1.74 fps Average velocity 1.65 fpsWater surface elevation above msl Water surface elevation above msl
Left bank 509.60 fr Left bank 509.27 ftRight bank 509.58 ft Right bank 509.21 ft
Distance along the centerlinebetween cross sections13 & 14 312 ft
Distance along the centerlinebetween cross sections 15 & 16 1448 ft
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
19 REW 24 REW22 1.3 0.69 27 1.8 0.4327 3.1 1.23 32 4.7 1.2332 6.2 1.34 37 5.5 1.6337 6.1 1.27 42 5.5 1.9542 5.5 1.37 47 5.2 2.0047 5.5 1.66 52 5.0 2.2152 5.1 1.60 62 5.1 2.0162 4.6 1.92 72 5.1 1.9372 4.5 2.08 82 5.3 2.0282 4.5 2.11 92 5.6 2.0692 4.9 2.04 102 5.8 1.90
102 6.0 1.99 107 6.1 1.70107 6.1 1.96 112 6.4 1.57112 6.3 1.81 117 6.3 1.30117 5.6 1.58 122 6.0 0.71122 5.8 1.47 127 5.5 0.72127 3.0 1.39 132 4.8 0.17132 2.1 1.05 134 3.0 -0.42135 1.3 0.23 136 LEW138 LEW
99
APPENDIX A. Continued — Shelbyville
Cross Section Number 17 Cross Section Number 2Date of data collection 10/24/75 Date of data collection 5/11/77Measured discharge 939 cfs Measured discharge 1363 cfsCross-sectional area 650 sq ft Cross-sectional area 726.3 sq ftAverage velocity 1.44 fps Average velocity 1.79 fpsWater surface elevation above msl Water surface elevation above msl
Left bank 508.95 ft Left bank 513.21 ftRight bank 509.01 ft Right bank 513.24 ft
Distance along the centerlinebetween cross sections 16 & 17 1136 ft
Distance along the centerlinebetween cross sections 1 & 2 1300 ft
Distance from theright side lookingdownstream (ft)
Depth ofWater (ft)
Average velocityin the vertical
(fps)
Distance from theright side lookingdownstream (ft)
Depth ofWater (ft)
Average velocityin the vertical
(fps)
20 REW 13 REW24 5.5 0.49 18 6.5 0.9028 6.6 0.86 22 7.3 1.2132 6.7 0.77 26 7.2 1.2138 6.7 1.17 30 7.4 1.6244 8.6 1.47 35 7.8 1.5850 9.2 1.62 40 7.8 2.1956 9.1 1.71 45 7.6 2.1062 9.1 1.97 50 7.3 2.4168 9.0 1.93 55 7.4 2.1974 8.7 1.85 60 7.5 2.4580 8.1 1.76 65 7.0 2.2785 7.8 1.55 70 6.6 2.4990 7.5 1.28 75 6.5 2.2995 7.1 1.22 80 6.2 2.31
100 6.2 0.89 85 6.1 1.97105 4.5 0.81 90 6.1 2.32109 LEW 95 5.6 1.93
100 5.5 1.94Cross Section Number 1 5/11/77 105 5.5 1.90Date of data collection 1423 cfs 110 5.2 1.66Measured discharge 817.5 sq ft 115 5.0 1.37Cross-sectional area 1.74 fps 120 3.2 1.29Average velocity 125 LEW 1.05Water surface elevation above msl 128
Left bank 513.42 fr Cross Section Number 3Right bank 513.45 ft Date of data collection 5/11/77
Distance along the centerline Measured discharge 1378 cfsbetween cross sections 0 Cross-sectional area 725.0 sq ft
Average velocity 1.90 fpsWater surface elevation above msl
Left bank 513.11 ft
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)Right bank 513.10 ft
21 REW 0.28 Distance along the centerline26 2.3 0.58 between cross sections 2 & 3 400 ft30 6.3 1.4235 8.1 1.7440 8.6 1.8950 8.4 2.09
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)60 9.1 2.58 9.0 REW70 8.8 2.29 13 3.1 0.7675 8.6 2.53 18 6.0 1.0980 8.7 2.38 25 8.5 1.4785 8.6 2.35 30 8.5 1.7690 8.8 2.12 35 8.4 2.0995 9.0 1.99 40 8.4 2.37
100 10.0 1.46 45 7.9 2.48105 9.8 0.57 50 7.6 2.65110 8.6 -0.45 55 7.5 2.38115 6.6 -0.27 60 7.5 2.51118 5.2 65 7.5 2.23122 LEW 70 7.1 2.33
75 6.4 2.2280 6.2 2.2185 6.2 2.0290 5.9 2.0595 5.7 1.75
100 5.7 1.53105 5.4 1.39110 5.0 1.23115 4.2 1.09118 1.8 0.46121 LEW100
APPENDIX A. Continued — Shelbyville
Cross Section Number 4 Cross Section Number 7Date of data collection 5/11/77 Date of data collection 5/12/77Measured discharge 1419 cfs Measured discharge 1495 cfsCross-sectional area 773.8 sq ft Cross-sectional area 896.3 sq ftAverage velocity 1.83 fps Average velocity 1.67 fpsWater surface elevation above msl Water surface elevation above msl
Left bank 513.12 ft Left bank 512.50 ftRight bank 513.08 ft Right bank 512.45 ft
Distance along the centerlinebetween cross sections 3 & 4 363 ft
Distance along the centerlinebetween cross sections 5 & 7 1196 ft
Distance from theright side lookingdownstream (ft)
Depth ofWater (ft)
Average velocityin the vertical
(fps)
Distance from theright side lookingdownstream (ft)
Depth ofWater (ft)
Average velocityin the vertical
(fps)
3 REW 28 REW8 3.1 0.36 32 0.9 0.26
12 4.1 0.93 36 2.9 0.2816 4.5 1.09 40 4.7 0.5522 5.2 1.63 45 7.1 0.4128 5.2 1.59 50 9.3 0.9536 7.0 2.07 55 9.4 1.7344 7.4 2.05 60 10.0 1.7350 8.0 2.26 65 10.7 1.9955 8.1 2.08 70 11.6 1.8860 8.5 2.34 75 12.4 1.6665 8.4 2.27 80 13.9 1.9070 8.7 2.35 85 15.0 1.9075 9.5 2.23 90 14.8 1.9380 10.0 2.16 95 14.4 1.7785 10.5 2.13 100 13.7 1.8490 10.6 1.91 105 11.6 1.9695 9.4 1.44 110 8.6 1.97
100 7.3 1.32 114 6.8 1.88105 5.0 1.11 118 4.1 1.72108 4.2 0.42 124 LEW111 REW
Cross Section Number 5 Cross Section Number 8 5/12/77Date of data collection 5/11/77 Date of data collection 1399 cfsMeasured discharge 1469 cfs Measured discharge 712.5 sq ftCross-sectional area 746.3 sq ft Cross-sectional area 1.96 fpsAverage velocity 1.97 fps Average velocityWater surface elevation above msl Water surface elevation above msl
Left bank 512.88 ft Left bank 512.24 ftRight bank 512.93 ft Right bank 512.23 ft
Distance along the centerlinebetween cross sections 7 & 8 452 ft
Distance along the centerlinebetween cross sections 4 & 5
1016 ft
Distance from theright side lookingdownstream (ft)
Depth ofWater (ft)
Average velocityin the vertical
(fps)
Distance from theright side lookingdownstream (ft)
Depth ofWater (ft)
Average velocityin the vertical
(fps)
12 REW 7 REW14 4.5 1.89 12 2.2 0.2418 8.1 2.13 15 3.2 0.9422 10.1 2.18 20 4.5 1.1626 11.1 2.28 25 5.7 1.9230 11.4 2.37 30 5.9 2.2734 11.7 2.36 35 7.5 2.4138 12.0 2.32 40 7.9 2.4142 12.2 2.15 50 8.2 2.6246 12.3 2.01 60 8.3 2.5550 12.7 1.91 65 7.1 2.3455 12.2 1.76 70 6.6 2.6660 10.1 1.82 75 7.4 2.4665 8.6 1.83 80 7.6 2.3270 7.4 1.61 85 7.5 1.9674 6.5 1.43 90 7.3 1.8578 5.8 1.34 95 7.0 1.5682 5.4 1.21 100 7.1 1.2386 4.2 0.76 105 7.1 0.9090 3.8 0.62 110 5.1 0.5194 2.8 0.21 114 2.3 0.1598 1.9 0 119 LEW
106 LEW
101
APPENDIX A. Continued — Shelbyville
Cross Section Number 9 Cross Section Number 11Date of data collection 5/13/77 Date of data collection 5/13/77Measured discharge 1530 cfs Measured discharge 1436 cfsCross-sectional area 903.8 sq ft Cross-sectional area 775 sq ftAverage velocity 1.69 fps Average velocity 1.85 fpsWater surface elevation above msl Water surface elevation above msl
Left bank 512.24 ft Left bank 511.83 ftRight bank 512.27 ft Right bank 511.68 ft
Distance along the centerlinebetween cross sections 8 & 9 552 ft
Distance along the centerlinebetween cross sections 10 & 11 620 ft
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
Distance from theright side lookingdownstream (ft)
Depth ofwater(ft)
Average velocityin the vertical
(fps)
8 REW 12 REW 13 4.4 1.27 18 1.5 0.59 18 7.3 1.37 22 3.4 1.68 22 8.8 1.34 28 5.6 2.10 28 10.8 1.52 35 6.3 2.17 35 12.3 1.57 42 6.5 2.13 42 13.4 1.67 50 6.1 1.82 50 14..3 1.98 55 5.5 1.92 55 14.1 2.01 60 4.4 1.98 60 14.0 2.06 65 4.2 1.97 65 12.4 2.01 70 4.4 2.14 70 10.6 1.88 75 5.3 2.05 75 9.7 1.68 80 5.8 2.25 80 7.9 1.91 85 6.1 1.64 85 5.8 1.63 90 6.8 2.08 90 4.4 1.34 95 8.1 1.98 95 3.8 1.35 100 8.9 1.99100 3.3 1.27 105 9.3 1.83105 2.8 1.41 110 9.5 1.90112 LEW 115 9.1 1.71
120 8.0 1.71Cross Section Number 10 125 8.0 1.61Date of data collection 5/13/77 130 6.6 1.37Measured discharge 1391 cfs 135 5.1 1.53Cross-sectional area 712.5 sq ft 137 3.3 1.14Average velocity 1.95 fps 142 LEWWater surface elevation above msl Cross Section Number 12
Left bank 511.95 fr Date of data collection Number 5/13/77Right bank 511.94 ft Measured discharge 1406 cfs
Cross-sectional area 698.8 sq ftDistance along the centerlinebetween cross sections 9 & 10 420 ft Average velocity 2.01 fps
Water surface elevation above mslLeft bank 511.35 ft
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps) Right bank 511.31 ft10 REW Distance along the centerline 972 ft15 3.7 0.68 between cross sections 11 & 1220 6.8 1.5024 8.4 2.0030 10.0 1.72
Distance from theright side lookingdownstream (ft)
Depth ofwater(ft)
Average velocityin the vertical
(fps)35 10.0 2.18 4 REW40 10.1 2.15 8 1.9 0.3145 9.0 2.21 12 3.5 0.9750 8.1 2.19 16 4.1 1.0655 7.3 2.01 20 6.0 1.6760 6.6 2.32 25 6.2 1.8065 5.8 2.19 30 7.3 2.1270 5.4 2.50 35 7.2 2.2675 4.9 2.35 40 7.2 2.3780 4.5 2.29 45 7.3 2.5385 4.4 2.11 50 7.2 2.5590 4.3 2.15 55 7.1 2.4395 4.3 2.13 60 7.5 2.59
100 4.4 2.00 65 8.1 2.42105 4.4 2.06 70 8.0 2.63110 4.2 1.72 75 8.0 2.27115 3.9 1.76 80 8.2 2.10120 3.5 1.66 85 8.5 2.25125 3.0 1.57 90 6.5 2.11130 2.2 0.78 95 6.9 1.62135 1.3 0.54 100 6.0 1.32140 LEW 105 5.0 0.86
110 2.2 0.53113 LEW102
APPENDIX A. Continued — Shelbyville
Cross Section Number 13 Cross Section Number 15Date of data collection 5/13/77 Date of data collection 5/16/77Measured discharge 1,454 cfs Measured discharge 1453 cfsCross-sectional area 640 sq ft Cross-sectional area 716.3 sq ftAverage velocity 2.27 fps Average velocity 2.03 fpsWater surface elevation above msl Water surface elevation above msl
Left bank 511.21 ft Left bank 511.00 ftRight bank 511.23 ft Right bank 510.98 ft
Distance along the centerlinebetween cross sections 12 & 13
320 ft Distance along the centerlinebetween cross sections 14 & 15
552 ft
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
9 REW 14 REW 13 3.6 1.85 18 2.0 0 17 6.1 2.68 22 2.9 0.14 22 9.7 2.24 26 3.7 0.27 28 12.4 2.47 30 3.8 0.93 34 11.9 2.55 35 3.5 1.31 40 10.3 2.50 40 4.7 1.51 46 9.3 2.43 45 6.7 1.61 55 8.0 2.42 50 6.9 1.99 60 7.5 2.33 55 8.5 2.13 65 6.6 2.43 60 8.6 2.20 70 5.8 2.28 65 8.7 2.29 75 4.4 2.33 70 9.5 2.18 80 4.2 2.17 75 11.0 2.45 85 3.5 1.85 80 11.4 2.39 90 3.4 1.73 85 12.1 2.06 95 2.9 1.44 90 12.0 2.29100 1.8 0.65 95 10.8 2.41107 LEW 100 8.7 2.50
105 5.6 2.51Cross Section Number 14 110 2.4 1.96Date of data collection 5/16/77 113 1.5 1.61Measured discharge 1338 cfs 116 LEWCross-sectional area 687.5 sq ftAverage velocity 1.95 fps Cross Section Number 17Water surface elevation above msl Date of data collection 5/16/77
Left bank 511.15 fr Measured discharge 1401 cfsRight bank 511.13 ft Cross-sectional area 785 sq ft
312 ft Average velocity 1.79 fpsDistance along the centerlinebetween cross sections 13 & 14 Water surface elevation above msl
Left bankRight bank
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
15 REW
Distance along the centerlinebetween cross sections 15 & 17
2584 ft
20 1.7 0.4524 3.0 0.8430 5.8 1.1435 7.5 1.74
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
40 7.3 1.78 14 REW45 6.7 2.25 20 5.150 6.5 2.45 24 6.255 6.3 2.56 28 7.4 1.360 6.0 2.51 32 7.1 1.4965 5.7 2.36 36 7.9 1.5770 5.5 2.21 40 9.2 1.7975 5.3 2.35 45 9.8 2.1680 5.3 2.11 50 9.6 2.3385 5.2 2.25 55 9.6 2.2790 5.4 2.10 60 9.5 2.3895 5.7 2.37 65 9.4 2.36
100 6.8 2.19 70 9.3 2.40105 7.0 2.10 75 9.2 2.27110 7.0 2 18 80 9.3 2.26115 6.5 2.07 85 8.9 1.88120 7.3 1.85 90 8.9 1.85125 6.1 1.71 95 8.6 1.65130 3.2 1.10 100 8.3 1.49135 2.0 0.41 105 6.0 0.92141 LEW 107 5.3 0.91
112 LEW
103
APPENDIX A. Continued — Shelbyville
Cross Section Number 1 Cross Section Number 3Date of data collection 3/20/78 Date of data collection 3/20/78Measured discharge 4555 cfs Measured discharge 4674 cfsCross-sectional area 1657.9 sq ft Cross-sectional area 1830.6 sq ftAverage velocity 2.75 fps Average velocity 2.55 fpsWater surface elevation above msl Water surface elevation above msl
Left bank 520.62 ft Left bank 520.38 ftRight bank 520.61 ft Right bank 520.41 ft
Distance along the centerlinebetween cross sections
0 Distance along the centerlinebetween cross sections 2 & 3
400 ft
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
0 REW 0 REW10 3.4 0.31 8 8.7 0.7418 7.6 0.95 13 11.9 1.0325 10.5 1.16 18 13.0 1.5130 14.8 1.56 28 13.2 2.4035 15.8 2.68 38 13.2 2.9240 16.1 3.21 48 17.3 2.6445 17.0 3.41 58 17.1 3.3055 16.0 3.77 68 16.0 3.4565 16.8 3.75 78 15.8 3.2575 16.6 3.70 88 14.7 3.3085 16.6 3.37 98 13.8 3.0895 16.6 3.38 108 12.9 2.84
105 16.5 2.17 118 11.2 2.08110 14.8 1.35 128 10.5 1.36115 13.1 1.11 138 5.0 0.24120 7.2 0.30 143 2.3 0.00125 3.0 0.00 148 2.2 0.00134 LEW 168 LEW
Cross Section Number 2 Cross Section Number 4Date of data collection 3/20/78 Date of data collection 3/21/78Measured discharge 4643 cfs Measured discharge 4620 cfsCross-sectional area 1646.7 sq ft Cross-sectional area 1682.8Average velocity 2.82 fps Average velocity 2.75 fpsWater surface elevation above msl Water surface elevation above msl
Left bank 520.40 ft Left bank 520.65 ftRight bank 520.42 ft Right bank 520.62 ft
Distance along the centerlinebetween cross sections 1 & 2
1300 ft Distance along the centerlinebetween cross sections 3 & 4
363 ft
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
0 REW 7 REW17 5.7 0.26 10 2.7 0.4622 8.8 0.81 20 7.4 1.1427 13.7 1.35 25 11.0 2.1432 15.3 2.01 30 14.0 2.8337 15.4 2.69 40 15.4 3.2747 15.7 3.23 50 15.6 3.6557 15.4 3.81 60 15.6 3.8767 14.5 3.92 70 16.5 3.8377 14.2 3.43 80 17.8 3.5587 13.6 3.53 90 17.9 3.1297 12.9 3.30 100 16.8 2.44
107 12.2 3.17 110 13.5 1.55117 12.3 2.81 115 10.8 1.11122 12.0 2.50 120 8.8 0.45127 10.8 2.11 125 6.6 0.30132 9.4 1.61 130 5.0 0.00137 6.5 1.17 135 LEW138 LEW
104
APPENDIX A. Continued — Shelbyville
Cross Section Number 5Date of data collection 3/22/78 Cross Section Number 7Measured discharge 3831 cfs Date of data collection 3/22/78Cross-sectional area 1475.9 sq ft Measured discharge 3556 cfsAverage velocity 2.60 fps Cross-sectional area 1610.4 sq ftWater surface elevation above msl Average velocity 2.21 fps
Left bank 519.43 ft Water surface elevation above mslRight bank 519.48 ft Left bank 519.29 ft
Right bank 519.24 ftDistance along the centerlinebetween cross sections 4 & 5
1016 ftDistance along the centerline
between cross sections 6 & 7748 ft
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
0 REW
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
3 6.9 1.03 0 REW6 9.6 1.52 20 2.4 0.40
11 14.4 2.00 25 3.3 0.8521 18.5 2.54 30 2.9 0.7031 20.0 2.89 36 4.5 0.6541 20.8 3.21 40 7.3 0.5551 18.0 3.29 45 10.4 0.4961 14.8 3.05 50 13.3 0.5671 11.9 2.75 60 15.0 1.8081 11.1 2.23 70 16.9 2.3291 7.6 1.95 80 20.3 2.81
101 6.2 1.32 90 21.3 2.56106 4.0 0.51 100 21.1 2.89111 2.6 0.17 110 18.8 2.74117 LEW 120 14.7 2.74
125 11.8 2.69Cross Section Number 6 130 8.8 2.12Date of data collection 3/21/78 134 LEWMeasured discharge 3366 cfsCross-sectional area 1668.2 sq ft Cross Section Number 8Average velocity 2.02 fps Date of data collection 3/22/78Water surface elevation above msl Measured discharge 3375 cfs
Left bank 520.40 ft Cross-sectional area 1493.9 sq ftRight bank 520.41 ft Average velocity 2.26 fps
Water surface elevation above mslDistance along the centerlinebetween cross sections 5 & 6
448 ftLeft bank 519.05 ftRight bank 519.09 ftDistance from the
right side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)Distance along the centerline
between cross sections 7 & 8452 ft
0 REW12 1.4 0.3122 4.1 0.2827 8.0 0.9337 12.7 1.68
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
47 15.1 2.66 0 REW57 18.6 2.76 7 6.6 0.0067 18.8 2.81 10 8.0 0.7877 17.8 2.60 15 10.3 1.1087 17.6 2.48 20 12.7 1.3597 18.3 2.02 25 11.8 1.49
107 16.6 1.49 35 16.6 1.96117 12.6 0.96 45 15.5 2.04127 9.8 0.99 55 13.7 2.42135 7.6 0.52 65 13.0 2.57139 LEW 75 12.4 2.53
85 12.7 3.1695 11.4 3.24
105 11.4 3.24115 9.5 2.69120 8.2 1.65125 6.7 1.56130 4.4 0.46138 LEW
105
APPENDIX A. Continued — Shelbyville
Cross Section Number 10 Cross Section Number 11Date of data collection 3/23/78 Date of data collection 3/23/78Measured discharge 3,532 cfs Measured discharge 3405 cfsCross-sectional area 1694.1 sq ft Cross-sectional area 1629.7 sq ftAverage velocity 2.09 fps Average velocity 2.09 fpsWater surface elevation above msl Water surface elevation above msl
Left bank 517.50 ft Left bank 517.40 ftRight bank 517.52 ft Right bank 517.30 ft
Distance along the centerlinebetween cross sections 8 & 10
972 ft Distance along the centerlinebetween cross sections 10 & 11
620 ft
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
10 4.6 0.90 30 2.4 0.5720 9.4 1.58 40 4.7 1.6830 16.8 3.29 50 5.6 2.0140 16.7 3.18 60 8.3 2.5350 15.9 2.89 70 9.5 2.4160 14.6 2.56 80 11.1 2.5770 14.4 2.72 90 12.8 2.7980 14.3 2.44 100 14.0 2.7590 12.1 2.89 110 14.5 2.65
100 9.9 2.16 120 14.7 2.45110 8.5 1.83 130 14.0 2.14120 7.6 0.83 140 14.0 1.90130 7.3 0.45 150 15.5 1.19140 6.4 0.29 160 13.6 1.34150 5.3 0.13 170 7.9 0.98160 5.1 0.00 175 4.1 1.06172 LEW 177 LEW
106
APPENDIX B. VELOCITY DISTRIBUTION DATA, KASKASKIA RIVERBELOW LAKE CARLYLE
Cross Section Number 1Date of data collection 5/17/77 Cross Section Number 3Measured discharge 285 cfs Date of data collection 5/17/77Cross-sectional area 243.8 sq ft Measured discharge 291 cfsAverage velocity 1.17 fps Cross-sectional area 253.8 sq ftWater surface elevation above msl Average velocity 1.15 fps
Left bank 407.23 ft Water surface elevation above mslRight bank 407.23 ft Left bank
Right bankDistance along the centerlinebetween cross sections
0900 ftDistance along the centerline
between cross sections 2 & 3Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
7 LEW
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
12 1.6 0.85 10 REW18 3.0 1.02 20 0.5 024 2.7 1.07 25 0.8 030 2.1 1.02 30 1.2 0.2536 1.8 1.05 35 1.8 0.5242 1.4 1.05 40 2.1 0.7650 1.6 1.16 45 2.6 0.8855 1.8 1.37 50 2.9 0.9460 1.9 1.44 55 3.2 1.2265 1.8 1.63 60 3.3 1.2870 2.0 1.76 65 3.7 1.2380 2.0 1.81 70 3.9 1.2185 1.9 1.87 75 3.9 1.3690 2.0 1.72 80 3.8 1.4695 1.9 1.45 85 4.3 1.44
100 1.9 1.52 90 4.2 1.44105 1.6 1.47 95 4.2 1.36110 2.3 1.19 100 3.0 1.35115 2.2 0.96 103 2.2 1.04120 1.9 0.59 106 LEW125 2.1 0.19128 1.8 0.34 Cross Section Number 4131 REW Date of data collection 5/17/77
Measured discharge 277 cfsCross Section Number 2 Cross-sectional area 188.8 sq ftDate of data collection 5/17/77 Average velocity 1.47 fpsMeasured discharge 287 cfs Water surface elevation above mslCross-sectional area 217.5 sq ft Left bankAverage velocity 1.32 fps Right bankWater surface elevation above msl
Left bankDistance along the centerline
between cross sections 3 & 4660 ft
Right bankDistance along the centerline
between cross sections 1 & 21200 ft Distance from the
right side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
17 REW30 0.6 0.44
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)35 0.9 0.88
6 REW 40 1.4 0.8610 2.2 0.57 45 1.8 0.9814 2.2 0.84 50 2.2 1.1820 1.9 1.01 55 2.2 1.4025 2.0 1.01 60 2.2 1.5630 1.9 1.55 65 2.5 1.6235 2.0 1.62 70 2.9 1.6040 2.1 1.83 75 3.2 1.6045 2.1 1.90 80 3.4 1.5750 2.1 1.97 85 3.3 1.5255 2.1 1.82 90 3.5 1.5460 2.2 1.87 95 3.3 1.4965 2.1 1.83 100 3.4 1.5570 2.2 1.83 105 3.0 1.4175 2.1 1.51 108 1.4 0.7980 2.1 1.54 111 LEW85 2.2 1.5890 1.9 1.3595 1.9 1.22
100 1.6 0.85105 1.5 0.37109 1.2 0.15112 LEW
107
APPENDIX B. Continued — Carlyle
Cross Section Number 5 Cross Section Number 7Date of data collection 5/17/77 Date of data collection 5/17/77Measured discharge 284 cfs Measured discharge 289 cfsCross-sectional area 333.8 sq ft Cross-sectional area 430 sq ftAverage velocity 0.85 fps Average velocity 0.67 fpsWater surface elevation above msl Water surface elevation above msl
Left bank Left bankRight bank Right bank
Distance along the centerlinebetween cross sections 4 & 5
500 ft Distance along the centerlinebetween cross sections 6 & 7
282 ft
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
5 REW14 REW 0.12 8 2.1 0.4117 2.0 0.28 12 3.7 0.6322 3.6 0.88 16 4.4 0.8528 4.1 1.26 20 6.2 0.9334 4.2 1.31 25 7.6 0.9140 4.2 1.34 30 8.0 0.8745 4.2 1.34 35 8.3 0.8850 4.2 1.32 40 7.9 0.7455 4.4 1.29 45 7.3 0.7160 4.6 1.24 50 6.9 0.5865 4.8 1.01 55 6.2 0.6270 5,0 0.64 60 5.4 0.6575 4.4 0.38 65 4.4 0.5480 4.5 0.23 70 4.0 0.3385 3.6 0.17 75 2.9 0.1290 2.9 0.06 83 LEW93 2.599 LEW
Cross Section Number 8Cross Section Number 6 Date of data collection 5/18/77Date of data collection 5/18/77 Measured discharge 277 cfsMeasured discharge 305 cfs Cross-sectional area 268.75 sq ftCross-sectional area 448.8 sq ft Average velocity 1.03 fpsAverage velocity 0.68 fps Water surface elevation above mslWater surface elevation above msl Left bank
Left bank Right bank
Right bank Distance along the centerlinebetween cross sections 7 & 8
568 ftDistance along the centerline
between cross sections 5 & 6 680 ft
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
4 REW7 1.6 0.42
4 REW 11 2.9 0.747 2.3 0.15 15 3.3 0.91
11 3.9 0.44 20 4.7 0.5615 5.3 0.39 25 4.8 0.9820 6.3 0.71 30 3.9 1.2725 6.9 0.72 35 4.4 1.0030 7.1 0.72 40 4.4 1.3435 7.1 0.78 45 3.9 1.1840 7.2 0.92 50 3.5 1.1945 6.9 0,95 55 2.7 1.4250 6.4 0.93 60 2.7 1.4255 5.9 0.85 65 2.5 1.2860 5.6 0.82 70 3.2 1.0365 5.6 0.74 75 2.3 0.9370 4.9 0.60 80 1.7 0.8175 4.1 0.37 85 1.4 0.6180 2.7 0.16 90 1.1 0.3590 0.9 0.16 95 0.6 0.2595 LEW 98 LEW
108
APPENDIX B. Continued — Carlyle
Cross Section Number 10Date of data collection 5/18/77 Cross Section Number 14Measured discharge 296 cfs Date of data collection 5/19/77Cross-sectional area 353.8 sq ft Measured discharge 286 cfsAverage velocity 0.84 fps Cross-sectional area 387.5 sq ftWater surface elevation above msl Average velocity 0.74 fps
Left bank Water surface elevation above mslRight bank Left bank
Right bankDistance along the centerlineetween cross sections 8 & 10
1660 ftDistance along the centerline
between cross sections 11 & 144624 ft
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
10 REW
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
14 2.1 0.52 7 REW18 2.2 0.79 11 1.5 0.022 2.3 1.07 15 2.5 0.1426 2.7 1.35 20 3.3 0.3730 2.9 1.36 25 3.7 0.5635 3.3 1.44 30 4.3 0.6040 3.6 1.53 35 4.6 0.8545 3.8 1.47 40 4.8 0.8350 3.9 1.43 45 4.4 0.9855 4.0 1.43 50 4.5 0.9960 4.1 1.38 55 4.4 1.1665 4.2 0.67 60 4.3 1.1370 4.4 0.55 65 4.2 1.0975 4.5 0.23 70 4.3 1.2080 4.9 0.36 75 4.3 1.1785 5.0 0.79 80 4.4 0.9990 4.8 0.30 85 4.6 0.6395 4.3 0.20 90 4.6 0.32
100 3.5 0.22 95 4.2 0.10105 2.3 0.27 100 3.2 0.10108 1.0 0 105 2.1 0.20113 LEW 108 LEW
Cross Section Number 11 Cross Section Number 15Date of data collection 5/19/77 Date of data collection 5/19/77Measured discharge 286 cfs Measured discharge 283 cfsCross-sectional area 407.5 sq ft Cross-sectional area 400 sq ftAverage velocity 0.70 fps Average velocity 0.71 fpsWater surface elevation above msl Water surface elevation above msl
Left bank Left bankRight bank Right bank
Distance along the centerlinebetween cross sections 10 & 11
1200 ft Distance along the centerlinebetween cross sections 14 & 15
2370 ft
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
6 REW 3 REW10 2.1 0 7 2.9 0.1415 3.3 0.11 12 3.9 0.2220 4.1 0.22 18 3.6 0.4725 4.1 0.32 26 3.8 0.6730 4.7 0.62 32 3.6 0.8635 5.1 0.63 40 3.7 0.7940 5.3 0.85 48 3.7 0.8345 5.2 0.95 55 3.5 0.9150 5.1 1.01 60 3.6 0.8955 5.1 1.04 65 3.7 0.9660 5.1 1.09 70 3.6 0.9765 4.8 0.92 75 3.6 0.8970 4.2 0.81 80 3.7 1.0275 5.2 0.85 85 3.6 0.9380 5.4 0.63 90 3.3 0.6985 5.1 0.63 95 3.0 0.8590 4.4 0.59 100 2.9 0.7395 3.0 0.39 105 2.7 0.5699 1.6 0.28 110 3.1 0.39
102 LEW 115 2.6 0.59120 2.1 0.42124 LEW
109
APPENDIX B. Continued — Carlyle
Cross Section Number 1 Cross Section Number 3Date of data collection 12/8/75 Date of data collection 12/11/75Measured discharge 2143 cfs Measured discharge 2200 cfsCross-sectional area 1136.2 sq ft Cross-sectional area 1047.8 sq ftAverage velocity 1.89 fps Average velocity 2.10 fpsWater surface elevation above msl Water surface elevation above msl
Left bank 414.08 ft Left bank 413.85 ftRight bank 404.05 ft Right bank 413.86 ft
Distance along the centerlinebetween cross sections
0 Distance along the centerlinebetween cross sections 2 & 3
900 ft
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
14 REW 34 REW20 3.85 0,95 41 4.1 0.9525 7.25 0.98 48 6.9 1.3130 8.25 0.95 55 8.3 1.7135 9.40 1.18 62.5 8.4 1.7140 9.55 1.33 70 9.3 2.1250 8.70 2.03 80 9.7 2.2460 8.00 2.14 90 9.5 2.3070 8.30 2.51 100 10.1 2.3080 8.50 2.37 110 10.5 2.6290 8.70 2.68 120 10.8 2.72
100 8.70 2.49 130 11.1 2.32110 8.55 2.32 137.5 10.6 2.01120 9.40 1.95 145 7.6 1.56130 9.70 1.80 150 5.4 1.48135 9.90 1.68 153 3.9 1.09140 9.90 1.35 158 LEW145 8.70 1.23150 6.30 0.77153 2.70 0.43 Cross Section Number 4157 LEW Date of data collection 12/11/75
Measured discharge 2228 cfsCross Section Number 2 Cross-sectional area 1127.3 sq ftDate of data collection 12/11/75 Average velocity 1.98 fpsMeasured discharge 2210 cfs Water surface elevation above mslCross-sectional area 971.3 sq ft Left bank 413.81 ftAverage velocity 2.28 fps Right bank 413.80 ftWater surface elevation above msl
Left bank 413.88 ftDistance along the centerline
between cross sections 3 & 4660 ft
Right bank 413.88 ftDistance along the centerline
between cross sections 1 & 21200 ft Distance from the
right side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
26 REW34 2.7 0.56
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)40 4.4 1.14
14 REW 48 6.4 1.2121 4.1 0.51 55 7.5 1,7526 7.7 1.26 65 7.9 2.2634 9.0 2.08 75 8.7 2.2142 8.9 2.29 85 8.8 2.4650 8.9 2.49 95 10.0 2.4160 8.9 3.08 105 10.0 2.4565 8.9 3.20 115 10.5 2.5670 8.9 3.18 125 9.8 2.3580 8.9 3.25 132.5 10.3 2.1490 8.9 2.87 140 10.4 1.37
100 8.9 2.18 147.5 10.3 1.17107 8.2 1.60 155 8.9 1.31115 7.4 1.63 160 5.6 1.56122 7.5 1.35 166 LEW127 7.7 1.25152 5.5 0.82136 LEW
110
APPENDIX B. Continued — Carlyle
Cross Section Number 5 Cross Section Number 7Date of data collection 12/9/75 Date of data collection 12/9/75Measured discharge 2169 cfs Measured discharge 2161 cfsCross-sectional area 1141.7 sq ft Cross-sectional area 1052.3 sq ftAverage velocity 1.90 fps Average velocity 2.05 fpsWater surface elevation above msl Water surface elevation above msl
Left bank 413.78 ft Left bank 413.75 ftRight bank 413.81 ft Right bank 413.76 ft
Distance along the centerlinebetween cross sections 4 & 5
500 ft Distance along the centerlinebetween cross sections 6 & 7
282 ft
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
8 REW 20 REW14 2.9 0.43 27 4.7 1.2820 4.85 0.75 32 8.3 1.4230 7.1 1.18 40 12.3 1.8740 8.4 1.29 48 14.1 2.2850 9.7 2.00 55 14.4 2.2660 11.4 2.63 65 12.0 1.9470 11.9 2.81 75 11.3 2.0880 12.0 2.71 85 10.2 2.3290 11.9 2.29 95 8.9 2.37
100 11.5 1.70 105 7.8 2.05110 10.8 1.19 115 6.5 2.04120 8.8 0.81 122 5.4 1.50130 8.8 0.97 128 4.4 1.14136 8.0 1.19 133 4.0 0.94150 LEW 142 LEW
Cross Section Number 6 Cross Section Number 8Date of data collection 12/9/75 Date of data collection 12/9/75Measured discharge 2112 cfs Measured discharge 1583 cfsCross-sectional area 1185.7 sq ft Cross-sectional area 934.1 sq ftAverage velocity 1.78 fps Average velocity 1.69 fpsWater surface elevation above msl Water surface elevation above msl
Left bank 413.76 ft Left bank 413.66 ftRight bank 413.80 Right bank 413.67 ft
Distance along the centerline between crosssections 5 & 6
680 ft Distance along the centerline between crosssections 7 & 8
568 ft
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
10 REW16 8.5 0.96 8 REW22 11.4 1.10 16 5.7 0.9030 13.5 1.42 22 9.5 1.3240 14.3 1.88 30 11.1 1.4650 14.5 2.14 40 11.5 1.8360 11.7 1.92 50 10.7 2.1570 11.1 2.03 65 10.0 2.0180 9.7 2.35 80 10.2 2.2190 8.9 2.26 95 9.2 2.13
100 7.6 2.11 105 8.8 1.95110 6.6 1.67 115 7.6 1.41120 5.9 1.25 125 5.6 1.27125 4.7 1.01 132 4.5 0.75130 3.6 0.76 137 3.2 0.86137 LEW 146 LEW
111
112
APPENDIX B. Continued — Carlyle
Cross Section Number 11 Cross Section Number 14Date of data collection 12/10/75 Date of data collection 12/10/75Measured discharge 2288 cfs Measured discharge 2183 cfsCross-sectional area 1083.2 sq ft Cross-sectional area 1254.9 sq ftAverage velocity 2.11 fps Average velocity 1.74 fpsWater surface elevation above msl Water surface elevation above msl
Left bank 413.28 ft Left bank 412.26 ftRight bank 413.29 ft Right bank 412.26 ft
Distance along the centerlinebetween cross sections 8 & 11
2860 ft Distance along the centerlinebetween cross sections 12 & 14
3296 ft
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
12 REW 17 REW22 2.2 0.51 21 3.6 0.3530 5.8 0.62 26 6.5 0.8138 8.2 1.40 30 7.4 1.0848 10.9 1.77 38 9.8 1.4155 10.8 1.97 46 11.1 1.5165 10.0 2.36 55 11.6 1.7675 10.0 2.60 65 12.1 2.1085 10.4 2.52 75 11.8 2.1295 9.9 2.56 85 11.5 2.37
105 10.7 2.37 95 11.6 2.23115 10.5 2.15 105 11.5 2.00122 10.1 2.05 115 12.2 1.66130 7.4 1.55 122 11.0 1.26136 4.9 1.17 130 9~3 1.33143 LEW 136 5.3 1.03
141 3.0 0.50147 LEW
Cross Section Number 12Date of data collection 12/10/75Measured discharge 2025 cfs Cross Section Number 15Cross-sectional area 993.9 sq ft Date of data collection 12/10/75Average velocity 2.04 fps Measured discharge 2165 cfsWater surface elevation above msl Cross-sectional area 1409.9 sq ft
Left bank 413.04 ft Average velocity 1.54 fpsRight bank 413.07 ft Water surface elevation above msl
Left bank 411.93 ftDistance along the centerlinebetween cross sections 11 & 12
1328 ftRight bank 411.91 ft
Distance along the centerlinebetween cross sections 14 & 15
2370 ftDistance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
14 REW18 3.2 1.48
Distance from theright side lookingdownstream (ft)
Depth ofWater(ft)
Average velocityin the vertical
(fps)
22 4.7 1.86 17 REW28 5.9 1.72 21 3.3 0.3836 7.2 2.41 28 9.4 0.9344 8.8 2.73 36 12.0 1.1452 10.1 2.69 44 11.3 1.6360 10.7 2.61 50 11.3 1.6670 11.6 2.48 60 11.3 1.8580 12.0 2.06 70 11.4 1.8390 12.0 2.08 80 11.6 2.09
100 12.2 1.70 90 11.4 1.97107 11.1 1.18 100 11.2 1.86110 12.1 1.51 110 11.0 1.70115 7.1 0.62 120 10.7 1.46120 2.7 0.51 130 10.6 1.30124 LEW 137 10.5 1.01
145 9.0 0.97150 6.4 0.66158 LEW
113
APPENDIX B. Continued — Carlyle
Cross Section Number 1 Cross Section Number 3Date of data collection 12/13/77 Date of data collection 12/13/77Measured discharge 3999 cfs Measured discharge 4027 cfsCross-sectional area 1738.9 sq ft Cross-sectional area 1594 sq ftAverage velocity 2.30 fps Average velocity 2.52 fpsWater surface elevation above msl Water surface elevation above msl
Left bank 417.62 ft Left bank 417.55 ftRight bank 417.65 ft Right bank 417.51 ft
Distance along the centerlinebetween cross sections
0 Distance along the centerlinebetween cross sections 2 & 3 900 ft
Distance from theright side lookingdownstream (ft)
Depth ofwater (ft)
Average velocityin the vertical
(fps)
Distance from theright side lookingdownstream (ft)
Depth ofwater (ft)
Average velocityin the vertical
(fps)0 REW 0 REW5 4.5 0.44 33 5.4 0.40
10 7.9 1.48 36 7.2 0.7515 9.6 1.37 41 9.3 1.1420 11.8 1.52 46 10.8 1.6325 13.3 1.95 51 11.0 1.7135 13.2 2.85 56 11.4 2.0445 12.4 2.92 61 11.7 2.1255 11.9 3.01 71 13.6 2.3965 12.3 3.10 81 13.8 2.8175 12.3 2.80 91 13.9 3.0185 12.5 2.66 101 15.0 3.3195 12.5 2.68 111 14.9 3.30105 13.0 2.64 121 15.1 3.09115 12.8 2.41 131 15.3 3.13125 13.2 2.01 141 13.4 2.41130 13.4 1.59 145 10.4 2.21135 13.0 1.26 149 8.7 1.55140 11.8 0.93 153 6.7 1.11145 6.5 0.36 156 LEW150 3.4 0.00156 LEW
Cross Section Number 4Date of data collection
Cross Section Number 2 Measured discharge 12/13/77Date of data collection 12/13/77 Cross-sectional area 3810 cfsMeasured discharge 4013 cfs Average velocity 1618.3 sq ftCross-sectional area 1491.3 sq ft Water surface elevation above msl 2.35 fpsAverage velocity 2.69 fps Left bankWater surface elevation above msl Right bank 417.55 ft
Left bank 417.63 ft Distance along the centerline 417.48 ftRight bank 417,57 ft between cross sections 3 & 4 660 ft
Distance along the centerlinebetween cross sections 1 & 2 1200 ft Distance from the Average velocity
right side looking Depth of in the verticalDistance from theright side lookingdownstream (ft)
Depth ofwater (ft)
Average velocityin the vertical
(fps)
downstream (ft) water (ft) (fps)
0 REW21 3.8 0.00
0 REW 26 5.3 0.1211 4.0 0.17 31 7.1 0.4416 5.3 0.27 36 8.1 0.8321 6.4 0.60 41 8.7 1.2926 8.2 0.77 51 9.8 9.9231 10.6 1.18 61 11.1 2.2536 12.7 1.75 71 10.8 2.4241 12.3 1.97 81 11.4 2.5151 12.4 2.51 91 13.1 2.6661 12.6 3.01 101 14.1 2.8371 12.7 3.36 111 14.4 2.9781 12.7 3.69 121 14.4 3.1491 12.7 3.66 131 14.3 3.09101 12.7 3.75 141 14.3 2.53111 12.7 3.33 149 14.1 2.39121 12.0 3.06 153 10.8 2.40126 11.4 2.71 158 8.4 1.90131 10.7 2.54 161 LEW136 8.6 1.58140 6.7 1.35144 LEW
114
APPENDIX B. Continued — Carlyle
Cross Section Number 5 Cross Section Number 7Date of data collection 12/14/77 Date of data collection 12/14/77Measured discharge 4013 cfs Measured discharge 3680 cfsCross-sectional area 2001.3 sq ft Cross-sectional area 1849.5 sq ftAverage velocity 2.01 fps Average velocity 1.99 fpsWater surface elevation above msl Water surface elevation above msl
Left bank 418.47 ft Left bank 418.22 ftRight bank 418.44 Right bank 418.27 ft
Distance along the centerlinebetween cross sections 4 & 5 500 ft
Distance along the centerlinebetween cross sections 6 & 7 282 ft
Distance from theright side lookingdownstream (ft)
Depth ofwater (ft)
Average velocityin the vertical
(fps)
Distance from theright side lookingdownstream (ft)
Depth ofwater (ft)
Average velocityin the vertical
(fps)
0 REW 4 REW32 7.0 0.67 6 7.0 0.3838 8.9 0.79 10 9.6 0.6043 8.8 0.98 15 14.0 0.9448 10.1 1.16 20 14.8 1.3253 10.7 1.45 25 15.1 1.8658 13.2 1.14 30 15.8 2.1863 14.7 1.53 40 17.9 2.4368 16.0 2.43 50 18.9 2.3573 16.3 2.44 60 19.8 2.3578 16.0 2.49 70 18.4 2.4083 16.1 2.55 80 16.3 2.3893 16.5 2.76 90 13.1 2.21103 16.8 2.79 100 12.2 2.31113 17.4 2.70 110 10.5 2.02123 17.3 2.57 115 9.5 1.79133 15.6 2.43 120 8.4 1.39138 13.8 2.07 125 7.5 0.87143 14.0 1.86 130 6.1 0.35148 12.8 1.77 135 3.7 0.19153 11.6 1.52 140 2.6 0.00158 10.0 0.97 145 1.8 0.00163 8.0 0.25 155 LEW168 5.4 0.29171 LEW
Cross Section Number 8Date of data collection 12/14/77
Cross Section Number 6 Measured discharge 3573 cfsDate of data collection 12/14/77 Cross-sectional area 1783.3 sq ftMeasured discharge 3799 cfs Average velocity 2.00 fpsCross-sectional area 1832.4 sq ft Water surface elevation above mslAverage velocity 2.07 fps Left bank 418.18 ftWater surface elevation above msl Right bank 418.25 ft
Left bank 418.39 ft Distance along the centerlineRight bank 418.49 ft between cross sections 7 & 8 568 ft
Distance along the centerlinebetween cross sections 5 & 6
680 ft Distance from theright side lookingdownstream (ft)
Depth ofwater (ft)
Average velocityin the vertical
(fps)Distance from theright side lookingdownstream (ft)
Depth ofwater (ft)
Average velocityin the vertical
(fps)1014
REW9.2 0.69
20 12.6 1.514 REW 25 13.8 1.79
11 11.4 1.49 35 16.4 1.9315 14.2 1.82 45 16.1 2.5220 15.9 2.14 55 14.9 2.5125 17.6 2.34 65 13.8 2.4935 18.5 2.51 75 14.0 2.4045 18.6 2.53 85 13.5 2.3855 18.8 2.55 95 13.2 2.4165 15.7 2.35 105 12.7 2.2475 14.1 2.17 115 11.6 2.0385 13.1 2.24 125 10.2 1.8895 11.7 2.19 135 8.4 1.34105 10.3 2.29 140 7.4 0.95115 9.8 1.81 145 6.5 0.53120 9.0 1.45 150 5.2 0.20125 8.5 1.01 155 2.8 0.00130 8.2 0.59 180 LEW135 6.9 0.19140 4.0 0.00145 3.1 0.00150 1.9 0.00160 LEW
APPENDIX B. Continued — Carlyle
Cross Section Number 10 Cross Section Number 12Date of data collection 12/15/77 Date of data collection 12/15/77Measured discharge 3460 cfs Measured discharge 3461 cfsCross-sectional area 1785.9 sq ft Cross-sectional area 1731.7 sq ftAverage velocity 1.94 fps Average velocity 2.00 fpsWater surface elevation above msl Water surface elevation above msl
Left bank 417.45 ft Left bank 417.14 ftRight bank 417.44 ft Right bank 417.19 ft
Distance along the centerlinebetween cross sections 8 & 10
1660 ft Distance along the centerlinebetween cross sections 11 & 12
1328 ft
Distance from theright side lookingdownstream (ft)
Depth ofwater (ft)
Average velocityin the vertical
(fps)
Distance from theright side lookingdownstream (ft)
Depth ofwater (ft)
Average velocityin the vertical
(fps)
0 REW 0 REW65 2.7 0.00 6 2.8 0.6375 5.9 0.68 11 5.8 0.7380 7.3 0.77 16 11.2 1.0485 8.7 1.08 21 13.6 1.5390 10.3 1.38 31 13.9 2.1195 12.2 1.66 41 14.3 2.20
100 12.8 1.85 51 14.9 2.22105 13.1 1.94 61 16.0 2.14110 13.5 2.22 71 16.6 1.96120 13.8 2.43 81 16.2 2.01130 14.3 2.55 91 13.2 2.46140 14.5 2.49 101 12.6 2.53150 15.0 2.28 111 12.5 2.32160 15.4 2.28 121 11.5 1.96170 15.7 2.25 125 12.1 1.61180 14.8 1.95 129 10.5 1.53185 13.8 1.69 133 9.1 1.28190 12.4 1.77 137 4.0 0.77195 11.2 1.30 143 LEW199 9.8 1.35203 8.0 0.98 Cross Section Number 14208 6.8 0.44 Date of data collection 12/15/77213 LEW Measured discharge 3388 cfs
Cross Section Number 11 Cross-sectional area 1937.9 sq ftDate of data collection 12/15/77 Average velocity 1.75 fpsMeasured discharge 3297 cfs Water surface elevation above mslCross-sectional area 1790.1 sq ft Left bank 416.72 ftAverage velocity 1.84 fps Right bank 416.78 ftWater surface elevation above msl Distance along the centerline
Left bank 417.38 ft between cross sections 12 & 14 3296 ftRight bank 417.37 ft
Distance along the centerlinebetween cross sections 10 & 11
1200 ft Distance from theright side lookingdownstream (ft)
Depth ofwater (ft)
Average velocityin the vertical
(fps)Distance from theright side lookingdownstream (ft)
Depth ofwater (ft)
Average velocityin the vertical
(fps)
0712
REW5.27.9
0.240.69
0 REW 17 10.0 0.9914 4.6 0.00 22 11.6 1.1619 6.6 0.00 32 14.6 1.4324 9.1 0.34 42 15.7 1.9229 11.4 0.84 52 16.4 2.1934 12.8 1.23 62 16.4 2.3639 14.6 1.49 72 16.2 2.3849 16.2 2.09 82 16.0 2.2959 17.5 2.36 92 15.6 2.0569 17.2 2.19 102 16.0 1.9979 17.2 2.19 112 16.5 1.5989 16.7 2.42 122 14.3 1.3899 16.7 2.18 127 12.6 1.39
109 14.9 2.06 132 9.7 1.11119 14.6 1.84 137 7.0 0.40123 13.2 1.63 142 4.4 0.18127 10.8 1.72 148 2.7 0.00131 9.9 1.50 155.5 LEW136 6.8 0.36140 LEW 115
APPENDIX B. Concluded — Carlyle
Cross Section Number 15
Date of data collection 12/16/77Measured discharge 3442 cfsCross-sectional area 2149.6 sq ftAverage velocity 1.60 fpsWater surface elevation above msl
Left bank 416.82 ftRight bank 416.80 ft
Distance along the centerlinebetween cross sections 14 & 15 2370 ft
Distance from theright side lookingdownstream (ft)
Depth ofwater (ft)
Average velocityin the vertical
(fps)
0 REW6 2.8 0.0011 5.2 0.0816 8.8 0.6721 14.6 1.0926 15.7 1.4331 16.1 1.4736 16.0 1.5841 16.0 1.7051 16.1 2.1161 16.2 2.0071 16.1 2.1281 16.3 2.0791 16.1 1.96
101 16.5 1.79111 15.9 1.74121 15.4 1.35131 15.1 1.29136 14.5 1.17141 12.8 0.93145 10.7 0.90149 8.5 0.49153 5.2 0.11159 LEW
116
